Algebra Examples

${(\cos (90) + i \sin (90))}^{6}$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\cos (90)$ is $0$ .

${(0 + i \sin (90))}^{6}$

Step 1.2

The exact value of $\sin (90)$ is $1$ .

${(0 + i \cdot 1)}^{6}$

Step 1.3

Multiply $i$ by $1$ .

${(0 + i)}^{6}$

${(0 + i)}^{6}$

Step 2

Simplify the expression.

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Step 2.1

Add $0$ and $i$ .

$i^{6}$

Step 2.2

Factor out $i^{4}$ .

$i^{4} i^{2}$

$i^{4} i^{2}$

Step 3

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

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Step 3.1

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

${(i^{2})}^{2} i^{2}$

Step 3.2

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

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

Step 3.3

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

$1 i^{2}$

$1 i^{2}$

Step 4

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

$i^{2}$

Step 5

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

$- 1$

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