Algebra Examples

$i^{0} \cdot i^{1} \cdot i^{2} \cdot i^{3} \cdot i^{4}$

Step 1

Anything raised to $0$ is $1$ .

$1 \cdot i^{1} \cdot i^{2} \cdot i^{3} \cdot i^{4}$

Step 2

Multiply $i^{1}$ by $1$ .

$i^{1} \cdot i^{2} \cdot i^{3} \cdot i^{4}$

Step 3

Simplify.

$i \cdot i^{2} \cdot i^{3} \cdot i^{4}$

Step 4

Rewrite $i^{2}$ as $- 1$ .

$i \cdot - 1 \cdot i^{3} \cdot i^{4}$

Step 5

Move $- 1$ to the left of $i$ .

$- 1 \cdot i \cdot i^{3} \cdot i^{4}$

Step 6

Rewrite $- 1 i$ as $- i$ .

$- i \cdot i^{3} \cdot i^{4}$

Step 7

Factor out $i^{2}$ .

$- i \cdot (i^{2} \cdot i) \cdot i^{4}$

Step 8

Rewrite $i^{2}$ as $- 1$ .

$- i \cdot (- 1 \cdot i) \cdot i^{4}$

Step 9

Rewrite $- 1 i$ as $- i$ .

$- i \cdot (- i) \cdot i^{4}$

Step 10

Multiply $- i (- i)$ .

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Step 10.1

Multiply $- 1$ by $- 1$ .

$1 i i \cdot i^{4}$

Step 10.2

Raise $i$ to the power of $1$ .

$1 (i^{1} i) \cdot i^{4}$

Step 10.3

Raise $i$ to the power of $1$ .

$1 (i^{1} i^{1}) \cdot i^{4}$

Step 10.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$1 i^{1 + 1} \cdot i^{4}$

Step 10.5

Add $1$ and $1$ .

$1 i^{2} \cdot i^{4}$

Step 10.6

Multiply $i^{2}$ by $1$ .

$i^{2} \cdot i^{4}$

Step 11

Rewrite $i^{2}$ as $- 1$ .

$- 1 \cdot i^{4}$

Step 12

Rewrite $i^{4}$ as $1$ .

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Step 12.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 1 \cdot {(i^{2})}^{2}$

Step 12.2

Rewrite $i^{2}$ as $- 1$ .

$- 1 \cdot {(- 1)}^{2}$

Step 12.3

Raise $- 1$ to the power of $2$ .

$- 1 \cdot 1$

Step 13

Multiply $- 1$ by $1$ .

$- 1$