Trigonometry Examples

$i^{99} - i^{3}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{99}$ as ${(i^{4})}^{24} (i^{2} \cdot i)$ .

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Step 1.1.1

Factor out $i^{96}$ .

$i^{96} i^{3} - i^{3}$

Step 1.1.2

Rewrite $i^{96}$ as ${(i^{4})}^{24}$ .

${(i^{4})}^{24} i^{3} - i^{3}$

Step 1.1.3

Factor out $i^{2}$ .

${(i^{4})}^{24} (i^{2} \cdot i) - i^{3}$

${(i^{4})}^{24} (i^{2} \cdot i) - i^{3}$

Step 1.2

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

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Step 1.2.1

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

${({(i^{2})}^{2})}^{24} (i^{2} \cdot i) - i^{3}$

Step 1.2.2

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

${({(- 1)}^{2})}^{24} (i^{2} \cdot i) - i^{3}$

Step 1.2.3

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

$1^{24} (i^{2} \cdot i) - i^{3}$

$1^{24} (i^{2} \cdot i) - i^{3}$

Step 1.3

One to any power is one.

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

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

$- i - i^{3}$

Step 1.7

Factor out $i^{2}$ .

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

Step 1.8

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

$- i - (- 1 \cdot i)$

Step 1.9

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

$- i - - i$

Step 1.10

Multiply $- 1$ by $- 1$ .

$- i + 1 i$

Step 1.11

Multiply $i$ by $1$ .

$- i + i$

$- i + i$

Step 2

Add $- i$ and $i$ .

$0$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$