Trigonometry Examples

$2 (\cos (45 °) + i \sin (45 °))$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\cos (45 °)$ is $\frac{\sqrt{2}}{2}$ .

$2 (\frac{\sqrt{2}}{2} + i \sin (45 °))$

Step 1.2

The exact value of $\sin (45 °)$ is $\frac{\sqrt{2}}{2}$ .

$2 (\frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2})$

Step 1.3

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

$2 (\frac{\sqrt{2}}{2} + \frac{i \sqrt{2}}{2})$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$2 \frac{\sqrt{2}}{2} + 2 \frac{i \sqrt{2}}{2}$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Cancel the common factor.

$2 \frac{\sqrt{2}}{2} + 2 \frac{i \sqrt{2}}{2}$

Step 2.2.2

Rewrite the expression.

$\sqrt{2} + 2 \frac{i \sqrt{2}}{2}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

$\sqrt{2} + 2 \frac{i \sqrt{2}}{2}$

Step 2.3.2

Rewrite the expression.

$\sqrt{2} + i \sqrt{2}$