Basic Math Examples

$7 i^{6} - 3 i^{4} + 5 i^{3} + \sqrt{16} i^{5}$

Step 1

Simplify each term.

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Step 1.1

Factor out $i^{4}$ .

$7 (i^{4} i^{2}) - 3 i^{4} + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.2

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

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Step 1.2.1

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

$7 ({(i^{2})}^{2} i^{2}) - 3 i^{4} + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.2.2

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

$7 ({(- 1)}^{2} i^{2}) - 3 i^{4} + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.2.3

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

$7 (1 i^{2}) - 3 i^{4} + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.3

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

$7 i^{2} - 3 i^{4} + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.4

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

$7 \cdot - 1 - 3 i^{4} + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.5

Multiply $7$ by $- 1$ .

$- 7 - 3 i^{4} + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.6

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

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Step 1.6.1

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

$- 7 - 3 {(i^{2})}^{2} + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.6.2

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

$- 7 - 3 {(- 1)}^{2} + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.6.3

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

$- 7 - 3 \cdot 1 + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.7

Multiply $- 3$ by $1$ .

$- 7 - 3 + 5 i^{3} + \sqrt{16} i^{5}$

Step 1.8

Factor out $i^{2}$ .

$- 7 - 3 + 5 (i^{2} \cdot i) + \sqrt{16} i^{5}$

Step 1.9

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

$- 7 - 3 + 5 (- 1 \cdot i) + \sqrt{16} i^{5}$

Step 1.10

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

$- 7 - 3 + 5 (- i) + \sqrt{16} i^{5}$

Step 1.11

Multiply $- 1$ by $5$ .

$- 7 - 3 - 5 i + \sqrt{16} i^{5}$

Step 1.12

Rewrite $16$ as $4^{2}$ .

$- 7 - 3 - 5 i + \sqrt{4^{2}} i^{5}$

Step 1.13

Pull terms out from under the radical, assuming positive real numbers.

$- 7 - 3 - 5 i + 4 i^{5}$

Step 1.14

Factor out $i^{4}$ .

$- 7 - 3 - 5 i + 4 (i^{4} i)$

Step 1.15

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

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Step 1.15.1

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

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

Step 1.15.2

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

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

Step 1.15.3

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

$- 7 - 3 - 5 i + 4 (1 i)$

Step 1.16

Multiply $i$ by $1$ .

$- 7 - 3 - 5 i + 4 i$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $3$ from $- 7$ .

$- 10 - 5 i + 4 i$

Step 2.2

Add $- 5 i$ and $4 i$ .

$- 10 - i$