Find the Complex Conjugate 3(cos(pi)+isin(pi))

$3 (\cos (π) + i \sin (π))$

Step 1

Simplify each term.

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.

$3 (- \cos (0) + i \sin (π))$

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

$3 (- 1 \cdot 1 + i \sin (π))$

Multiply $- 1$ by $1$ .

$3 (- 1 + i \sin (π))$

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

$3 (- 1 + i \sin (0))$

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

$3 (- 1 + i \cdot 0)$

Multiply $i$ by $0$ .

$3 (- 1 + 0)$

Step 2

Add $- 1$ and $0$ .

$3 \cdot - 1$

Step 3

Multiply $3$ by $- 1$ .

$- 3$

Step 4

Since there are no imaginary terms, the complex conjugate is the same as the simplified expression.

$- 3$

Find the Complex Conjugate 3(cos(pi)+isin(pi))

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