Algebra Examples

$z = 5 (\cos (π) + i \sin (π))$

Step 1

Simplify $5 (\cos (π) + i \sin (π))$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$z = 5 (- \cos (0) + i \sin (π))$

Step 1.1.2

The exact value of $\cos (0)$ is $1$ .

$z = 5 (- 1 \cdot 1 + i \sin (π))$

Step 1.1.3

Multiply $- 1$ by $1$ .

$z = 5 (- 1 + i \sin (π))$

Step 1.1.4

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$z = 5 (- 1 + i \sin (0))$

Step 1.1.5

The exact value of $\sin (0)$ is $0$ .

$z = 5 (- 1 + i \cdot 0)$

Step 1.1.6

Multiply $i$ by $0$ .

$z = 5 (- 1 + 0)$

Step 1.2

Simplify the expression.

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Step 1.2.1

Add $- 1$ and $0$ .

$z = 5 \cdot - 1$

Step 1.2.2

Multiply $5$ by $- 1$ .

$z = - 5$