Cálculo Ejemplos

${(\frac{1}{2} (\cos (\frac{π}{7}) + i \sin (\frac{π}{7})))}^{7}$

Paso 1

Simplifica cada término.

Toca para ver más pasos...

Paso 1.1

Evalúa $\cos (\frac{π}{7})$ .

${(\frac{1}{2} (0.90096886 + i \sin (\frac{π}{7})))}^{7}$

Paso 1.2

Evalúa $\sin (\frac{π}{7})$ .

${(\frac{1}{2} (0.90096886 + i \cdot 0.43388373))}^{7}$

Paso 1.3

Mueve $0.43388373$ a la izquierda de $i$ .

${(\frac{1}{2} (0.90096886 + 0.43388373 i))}^{7}$

Paso 2

Simplifica los términos.

Toca para ver más pasos...

Paso 2.1

Aplica la propiedad distributiva.

${(\frac{1}{2} \cdot 0.90096886 + \frac{1}{2} (0.43388373 i))}^{7}$

Paso 2.2

Combina $\frac{1}{2}$ y $0.90096886$ .

${(\frac{0.90096886}{2} + \frac{1}{2} (0.43388373 i))}^{7}$

Paso 3

Multiplica $\frac{1}{2} (0.43388373 i)$ .

Toca para ver más pasos...

Paso 3.1

Combina $0.43388373$ y $\frac{1}{2}$ .

${(\frac{0.90096886}{2} + \frac{0.43388373}{2} i)}^{7}$

Paso 3.2

Combina $\frac{0.43388373}{2}$ y $i$ .

${(\frac{0.90096886}{2} + \frac{0.43388373 i}{2})}^{7}$

Paso 4

Simplifica cada término.

Toca para ver más pasos...

Paso 4.1

Divide $0.90096886$ por $2$ .

${(0.45048443 + \frac{0.43388373 i}{2})}^{7}$

Paso 4.2

Factoriza $0.43388373$ de $0.43388373 i$ .

${(0.45048443 + \frac{0.43388373 (i)}{2})}^{7}$

Paso 4.3

Factoriza $2$ de $2$ .

${(0.45048443 + \frac{0.43388373 (i)}{2 (1)})}^{7}$

Paso 4.4

Separa las fracciones.

${(0.45048443 + \frac{0.43388373}{2} \cdot \frac{i}{1})}^{7}$

Paso 4.5

Divide $0.43388373$ por $2$ .

${(0.45048443 + 0.21694186 \frac{i}{1})}^{7}$

Paso 4.6

Divide $i$ por $1$ .

${(0.45048443 + 0.21694186 i)}^{7}$

Paso 5

Usa el teorema del binomio.

${0.45048443}^{7} + 7 \cdot {0.45048443}^{6} (0.21694186 i) + 21 \cdot {0.45048443}^{5} {(0.21694186 i)}^{2} + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6

Simplifica los términos.

Toca para ver más pasos...

Paso 6.1

Simplifica cada término.

Toca para ver más pasos...

Paso 6.1.1

Eleva $0.45048443$ a la potencia de $7$ .

$0.00376494 + 7 \cdot {0.45048443}^{6} (0.21694186 i) + 21 \cdot {0.45048443}^{5} {(0.21694186 i)}^{2} + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.2

Eleva $0.45048443$ a la potencia de $6$ .

$0.00376494 + 7 \cdot 0.00835754 (0.21694186 i) + 21 \cdot {0.45048443}^{5} {(0.21694186 i)}^{2} + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.3

Multiplica $7$ por $0.00835754$ .

$0.00376494 + 0.05850281 (0.21694186 i) + 21 \cdot {0.45048443}^{5} {(0.21694186 i)}^{2} + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.4

Multiplica $0.21694186$ por $0.05850281$ .

$0.00376494 + 0.01269171 i + 21 \cdot {0.45048443}^{5} {(0.21694186 i)}^{2} + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.5

Eleva $0.45048443$ a la potencia de $5$ .

$0.00376494 + 0.01269171 i + 21 \cdot 0.01855235 {(0.21694186 i)}^{2} + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.6

Multiplica $21$ por $0.01855235$ .

$0.00376494 + 0.01269171 i + 0.38959936 {(0.21694186 i)}^{2} + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.7

Aplica la regla del producto a $0.21694186 i$ .

$0.00376494 + 0.01269171 i + 0.38959936 ({0.21694186}^{2} i^{2}) + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.8

Eleva $0.21694186$ a la potencia de $2$ .

$0.00376494 + 0.01269171 i + 0.38959936 (0.04706377 i^{2}) + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.9

Reescribe $i^{2}$ como $- 1$ .

$0.00376494 + 0.01269171 i + 0.38959936 (0.04706377 \cdot - 1) + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.10

Multiplica $0.38959936 (0.04706377 \cdot - 1)$ .

Toca para ver más pasos...

Paso 6.1.10.1

Multiplica $0.04706377$ por $- 1$ .

$0.00376494 + 0.01269171 i + 0.38959936 \cdot - 0.04706377 + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.10.2

Multiplica $0.38959936$ por $- 0.04706377$ .

$0.00376494 + 0.01269171 i - 0.01833601 + 35 \cdot {0.45048443}^{4} {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.11

Eleva $0.45048443$ a la potencia de $4$ .

$0.00376494 + 0.01269171 i - 0.01833601 + 35 \cdot 0.04118311 {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.12

Multiplica $35$ por $0.04118311$ .

$0.00376494 + 0.01269171 i - 0.01833601 + 1.4414089 {(0.21694186 i)}^{3} + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.13

Aplica la regla del producto a $0.21694186 i$ .

$0.00376494 + 0.01269171 i - 0.01833601 + 1.4414089 ({0.21694186}^{3} i^{3}) + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.14

Eleva $0.21694186$ a la potencia de $3$ .

$0.00376494 + 0.01269171 i - 0.01833601 + 1.4414089 (0.0102101 i^{3}) + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.15

Factoriza $i^{2}$ .

$0.00376494 + 0.01269171 i - 0.01833601 + 1.4414089 (0.0102101 (i^{2} \cdot i)) + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.16

Reescribe $i^{2}$ como $- 1$ .

$0.00376494 + 0.01269171 i - 0.01833601 + 1.4414089 (0.0102101 (- 1 \cdot i)) + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.17

Reescribe $- 1 i$ como $- i$ .

$0.00376494 + 0.01269171 i - 0.01833601 + 1.4414089 (0.0102101 (- i)) + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.18

Multiplica $- 1$ por $0.0102101$ .

$0.00376494 + 0.01269171 i - 0.01833601 + 1.4414089 (- 0.0102101 i) + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.19

Multiplica $- 0.0102101$ por $1.4414089$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 35 \cdot {0.45048443}^{3} {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.20

Eleva $0.45048443$ a la potencia de $3$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 35 \cdot 0.09141961 {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.21

Multiplica $35$ por $0.09141961$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 3.19968636 {(0.21694186 i)}^{4} + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.22

Aplica la regla del producto a $0.21694186 i$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 3.19968636 ({0.21694186}^{4} i^{4}) + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.23

Eleva $0.21694186$ a la potencia de $4$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 3.19968636 (0.00221499 i^{4}) + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.24

Reescribe $i^{4}$ como $1$ .

Toca para ver más pasos...

Paso 6.1.24.1

Reescribe $i^{4}$ como ${(i^{2})}^{2}$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 3.19968636 (0.00221499 {(i^{2})}^{2}) + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.24.2

Reescribe $i^{2}$ como $- 1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 3.19968636 (0.00221499 {(- 1)}^{2}) + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.24.3

Eleva $- 1$ a la potencia de $2$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 3.19968636 (0.00221499 \cdot 1) + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.25

Multiplica $3.19968636 (0.00221499 \cdot 1)$ .

Toca para ver más pasos...

Paso 6.1.25.1

Multiplica $0.00221499$ por $1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 3.19968636 \cdot 0.00221499 + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.25.2

Multiplica $3.19968636$ por $0.00221499$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 21 \cdot {0.45048443}^{2} {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.26

Eleva $0.45048443$ a la potencia de $2$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 21 \cdot 0.20293622 {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.27

Multiplica $21$ por $0.20293622$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 4.26166072 {(0.21694186 i)}^{5} + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.28

Aplica la regla del producto a $0.21694186 i$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 4.26166072 ({0.21694186}^{5} i^{5}) + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.29

Eleva $0.21694186$ a la potencia de $5$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 4.26166072 (0.00048052 i^{5}) + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.30

Factoriza $i^{4}$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 4.26166072 (0.00048052 (i^{4} i)) + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.31

Reescribe $i^{4}$ como $1$ .

Toca para ver más pasos...

Paso 6.1.31.1

Reescribe $i^{4}$ como ${(i^{2})}^{2}$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 4.26166072 (0.00048052 ({(i^{2})}^{2} i)) + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.31.2

Reescribe $i^{2}$ como $- 1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 4.26166072 (0.00048052 ({(- 1)}^{2} i)) + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.31.3

Eleva $- 1$ a la potencia de $2$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 4.26166072 (0.00048052 (1 i)) + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.32

Multiplica $i$ por $1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 4.26166072 (0.00048052 i) + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.33

Multiplica $0.00048052$ por $4.26166072$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 7 \cdot 0.45048443 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.34

Multiplica $7$ por $0.45048443$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 3.15339103 {(0.21694186 i)}^{6} + {(0.21694186 i)}^{7}$

Paso 6.1.35

Aplica la regla del producto a $0.21694186 i$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 3.15339103 ({0.21694186}^{6} i^{6}) + {(0.21694186 i)}^{7}$

Paso 6.1.36

Eleva $0.21694186$ a la potencia de $6$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 3.15339103 (0.00010424 i^{6}) + {(0.21694186 i)}^{7}$

Paso 6.1.37

Factoriza $i^{4}$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 3.15339103 (0.00010424 (i^{4} i^{2})) + {(0.21694186 i)}^{7}$

Paso 6.1.38

Reescribe $i^{4}$ como $1$ .

Toca para ver más pasos...

Paso 6.1.38.1

Reescribe $i^{4}$ como ${(i^{2})}^{2}$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 3.15339103 (0.00010424 ({(i^{2})}^{2} i^{2})) + {(0.21694186 i)}^{7}$

Paso 6.1.38.2

Reescribe $i^{2}$ como $- 1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 3.15339103 (0.00010424 ({(- 1)}^{2} i^{2})) + {(0.21694186 i)}^{7}$

Paso 6.1.38.3

Eleva $- 1$ a la potencia de $2$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 3.15339103 (0.00010424 (1 i^{2})) + {(0.21694186 i)}^{7}$

Paso 6.1.39

Multiplica $i^{2}$ por $1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 3.15339103 (0.00010424 i^{2}) + {(0.21694186 i)}^{7}$

Paso 6.1.40

Reescribe $i^{2}$ como $- 1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 3.15339103 (0.00010424 \cdot - 1) + {(0.21694186 i)}^{7}$

Paso 6.1.41

Multiplica $3.15339103 (0.00010424 \cdot - 1)$ .

Toca para ver más pasos...

Paso 6.1.41.1

Multiplica $0.00010424$ por $- 1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i + 3.15339103 \cdot - 0.00010424 + {(0.21694186 i)}^{7}$

Paso 6.1.41.2

Multiplica $3.15339103$ por $- 0.00010424$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + {(0.21694186 i)}^{7}$

Paso 6.1.42

Aplica la regla del producto a $0.21694186 i$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + {0.21694186}^{7} i^{7}$

Paso 6.1.43

Eleva $0.21694186$ a la potencia de $7$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + 0.00002261 i^{7}$

Paso 6.1.44

Reescribe $i^{7}$ como $i^{4} (i^{2} \cdot i)$ .

Toca para ver más pasos...

Paso 6.1.44.1

Factoriza $i^{4}$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + 0.00002261 (i^{4} i^{3})$

Paso 6.1.44.2

Factoriza $i^{2}$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + 0.00002261 (i^{4} (i^{2} \cdot i))$

Paso 6.1.45

Reescribe $i^{4}$ como $1$ .

Toca para ver más pasos...

Paso 6.1.45.1

Reescribe $i^{4}$ como ${(i^{2})}^{2}$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + 0.00002261 ({(i^{2})}^{2} (i^{2} \cdot i))$

Paso 6.1.45.2

Reescribe $i^{2}$ como $- 1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + 0.00002261 ({(- 1)}^{2} (i^{2} \cdot i))$

Paso 6.1.45.3

Eleva $- 1$ a la potencia de $2$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + 0.00002261 (1 (i^{2} \cdot i))$

Paso 6.1.46

Multiplica $i^{2} \cdot i$ por $1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + 0.00002261 (i^{2} \cdot i)$

Paso 6.1.47

Reescribe $i^{2}$ como $- 1$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + 0.00002261 (- 1 \cdot i)$

Paso 6.1.48

Reescribe $- 1 i$ como $- i$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 + 0.00002261 (- i)$

Paso 6.1.49

Multiplica $- 1$ por $0.00002261$ .

$0.00376494 + 0.01269171 i - 0.01833601 - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 - 0.00002261 i$

Paso 6.2

Simplifica mediante la adición de términos.

Toca para ver más pasos...

Paso 6.2.1

Resta $0.01833601$ de $0.00376494$ .

$- 0.01457107 + 0.01269171 i - 0.01471693 i + 0.0070873 + 0.00204783 i - 0.00032872 - 0.00002261 i$

Paso 6.2.2

Simplifica mediante suma y resta.

Toca para ver más pasos...

Paso 6.2.2.1

Suma $- 0.01457107$ y $0.0070873$ .

$- 0.00748377 + 0.01269171 i - 0.01471693 i + 0.00204783 i - 0.00032872 - 0.00002261 i$

Paso 6.2.2.2

Resta $0.00032872$ de $- 0.00748377$ .

$- 0.0078125 + 0.01269171 i - 0.01471693 i + 0.00204783 i - 0.00002261 i$

Paso 6.2.3

Resta $0.01471693 i$ de $0.01269171 i$ .

$- 0.0078125 - 0.00202522 i + 0.00204783 i - 0.00002261 i$

Paso 6.2.4

Suma $- 0.00202522 i$ y $0.00204783 i$ .

$- 0.0078125 + 0.00002261 i - 0.00002261 i$

Paso 6.2.5

Resta $0.00002261 i$ de $0.00002261 i$ .

$- 0.0078125 0 i$

Paso 7

Esta es la forma trigonométrica de un número complejo donde $| z |$ es el módulo y $θ$ es el ángulo creado en el plano complejo.

$z = a + b i = | z | (\cos (θ) + i \sin (θ))$

Paso 8

El módulo de un número complejo es la distancia desde el origen en el plano complejo.

$| z | = \sqrt{a^{2} + b^{2}}$ donde $z = a + b i$

Paso 9

Sustituye los valores reales de $a = - 0.0078125$ y $b = 0$ .

$| z | = \sqrt{{(0)}^{2} + {(- 0.0078125)}^{2}}$

Paso 10

Obtén $| z |$ .

Toca para ver más pasos...

Paso 10.1

Eleva $0$ a la potencia de $2$ .

$| z | = \sqrt{0 + {(- 0.0078125)}^{2}}$

Paso 10.2

Eleva $- 0.0078125$ a la potencia de $2$ .

$| z | = \sqrt{0 + 0.00006103}$

Paso 10.3

Suma $0$ y $0.00006103$ .

$| z | = \sqrt{0.00006103}$

Paso 11

Evalúa la raíz.

$| z | = 0.0078125$

Paso 12

El ángulo del punto en el plano complejo es la inversa de la tangente de la parte compleja en la parte real.

$θ = \arctan (\frac{0}{- 0.0078125})$

Paso 13

Como la tangente inversa de $\frac{0}{- 0.0078125}$ produce un ángulo en el tercer cuadrante, el valor del ángulo es $3.14159265$ .

$θ = 3.14159265$

Paso 14

Sustituye los valores de $θ = 3.14159265$ y $| z | = 0.0078125$ .

$0.0078125 (\cos (3.14159265) + i \sin (3.14159265))$