Precalculus Examples

$3 (\cos (60 °) + i \sin (60 °)) + 2 (\cos (35 °) + i \sin (35 °))$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

The exact value of $\cos (60 °)$ is $\frac{1}{2}$ .

$3 (\frac{1}{2} + i \sin (60 °)) + 2 (\cos (35 °) + i \sin (35 °))$

Step 1.1.2

The exact value of $\sin (60 °)$ is $\frac{\sqrt{3}}{2}$ .

$3 (\frac{1}{2} + i \frac{\sqrt{3}}{2}) + 2 (\cos (35 °) + i \sin (35 °))$

Step 1.1.3

Combine $i$ and $\frac{\sqrt{3}}{2}$ .

$3 (\frac{1}{2} + \frac{i \sqrt{3}}{2}) + 2 (\cos (35 °) + i \sin (35 °))$

Step 1.2

Apply the distributive property.

$3 (\frac{1}{2}) + 3 \frac{i \sqrt{3}}{2} + 2 (\cos (35 °) + i \sin (35 °))$

Step 1.3

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} + 3 \frac{i \sqrt{3}}{2} + 2 (\cos (35 °) + i \sin (35 °))$

Step 1.4

Combine $3$ and $\frac{i \sqrt{3}}{2}$ .

$\frac{3}{2} + \frac{3 (i \sqrt{3})}{2} + 2 (\cos (35 °) + i \sin (35 °))$

Step 1.5

Apply the distributive property.

$\frac{3}{2} + \frac{3 i \sqrt{3}}{2} + 2 \cos (35 °) + 2 i \sin (35 °)$

Step 2

Reorder $\frac{3}{2} + \frac{3 i \sqrt{3}}{2}$ and $2 \cos (35 °)$ .

$2 \cos (35 °) + \frac{3}{2} + \frac{3 i \sqrt{3}}{2} + 2 i \sin (35 °)$