Calculus Examples

$z^{7} = {(\cos (30 °) + i \sin (30 °))}^{7}$

Step 1

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$z = \cos (30 °) + i \sin (30 °)$

Step 2

Simplify each term.

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Step 2.1

The exact value of $\cos (30 °)$ is $\frac{\sqrt{3}}{2}$ .

$z = \frac{\sqrt{3}}{2} + i \sin (30 °)$

Step 2.2

The exact value of $\sin (30 °)$ is $\frac{1}{2}$ .

$z = \frac{\sqrt{3}}{2} + i \frac{1}{2}$

Step 2.3

Combine $i$ and $\frac{1}{2}$ .

$z = \frac{\sqrt{3}}{2} + \frac{i}{2}$