Algebra Examples

$(2 + 4 i^{5}) + (1 - 9 i^{6}) - (3 + i^{7})$

Step 1

Remove parentheses.

$2 + 4 i^{5} + 1 - 9 i^{6} - (3 + i^{7})$

Step 2

Simplify each term.

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Step 2.1

Factor out $i^{4}$ .

$2 + 4 (i^{4} i) + 1 - 9 i^{6} - (3 + i^{7})$

Step 2.2

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

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Step 2.2.1

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

$2 + 4 ({(i^{2})}^{2} i) + 1 - 9 i^{6} - (3 + i^{7})$

Step 2.2.2

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

$2 + 4 ({(- 1)}^{2} i) + 1 - 9 i^{6} - (3 + i^{7})$

Step 2.2.3

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

$2 + 4 (1 i) + 1 - 9 i^{6} - (3 + i^{7})$

Step 2.3

Multiply $i$ by $1$ .

$2 + 4 i + 1 - 9 i^{6} - (3 + i^{7})$

Step 2.4

Factor out $i^{4}$ .

$2 + 4 i + 1 - 9 (i^{4} i^{2}) - (3 + i^{7})$

Step 2.5

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

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Step 2.5.1

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

$2 + 4 i + 1 - 9 ({(i^{2})}^{2} i^{2}) - (3 + i^{7})$

Step 2.5.2

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

$2 + 4 i + 1 - 9 ({(- 1)}^{2} i^{2}) - (3 + i^{7})$

Step 2.5.3

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

$2 + 4 i + 1 - 9 (1 i^{2}) - (3 + i^{7})$

Step 2.6

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

$2 + 4 i + 1 - 9 i^{2} - (3 + i^{7})$

Step 2.7

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

$2 + 4 i + 1 - 9 \cdot - 1 - (3 + i^{7})$

Step 2.8

Multiply $- 9$ by $- 1$ .

$2 + 4 i + 1 + 9 - (3 + i^{7})$

Step 2.9

Simplify each term.

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Step 2.9.1

Rewrite $i^{7}$ as $i^{4} (i^{2} \cdot i)$ .

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Step 2.9.1.1

Factor out $i^{4}$ .

$2 + 4 i + 1 + 9 - (3 + i^{4} i^{3})$

Step 2.9.1.2

Factor out $i^{2}$ .

$2 + 4 i + 1 + 9 - (3 + i^{4} (i^{2} \cdot i))$

Step 2.9.2

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

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Step 2.9.2.1

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

$2 + 4 i + 1 + 9 - (3 + {(i^{2})}^{2} (i^{2} \cdot i))$

Step 2.9.2.2

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

$2 + 4 i + 1 + 9 - (3 + {(- 1)}^{2} (i^{2} \cdot i))$

Step 2.9.2.3

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

$2 + 4 i + 1 + 9 - (3 + 1 (i^{2} \cdot i))$

Step 2.9.3

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

$2 + 4 i + 1 + 9 - (3 + i^{2} \cdot i)$

Step 2.9.4

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

$2 + 4 i + 1 + 9 - (3 - 1 \cdot i)$

Step 2.9.5

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

$2 + 4 i + 1 + 9 - (3 - i)$

Step 2.10

Apply the distributive property.

$2 + 4 i + 1 + 9 - 1 \cdot 3 - - i$

Step 2.11

Multiply $- 1$ by $3$ .

$2 + 4 i + 1 + 9 - 3 - - i$

Step 2.12

Multiply $- 1$ by $- 1$ .

$2 + 4 i + 1 + 9 - 3 + 1 i$

Step 2.13

Multiply $i$ by $1$ .

$2 + 4 i + 1 + 9 - 3 + i$

Step 3

Simplify by adding terms.

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Step 3.1

Add $2$ and $1$ .

$3 + 4 i + 9 - 3 + i$

Step 3.2

Simplify by adding and subtracting.

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Step 3.2.1

Add $3$ and $9$ .

$12 + 4 i - 3 + i$

Step 3.2.2

Subtract $3$ from $12$ .

$9 + 4 i + i$

Step 3.3

Add $4 i$ and $i$ .

$9 + 5 i$