Find the trigonometric form of $- 9 + 9 i$ .
A) $9 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)$
B) $\frac { 9 } { 2 } \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$
C) $9 \sqrt { 2 } \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$
D) $9 \sqrt { 2 } \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)$
E) $\frac { 9 } { 2 } \left( \cos \frac { 3 \pi } { 8 } + i \sin \frac { 3 \pi } { 8 } \right)$

Question

Quizplus · Accepted Answer

The magnitude of the complex number $-9 + 9i$ is $|z| = \sqrt{(-9)^2 + 9^2} = 9\sqrt{2}$. The angle $\theta$ in the complex plane, measured from the positive real axis, is $\frac{3\pi}{4}$ because the point lies in the second quadrant where both sine and cosine are positive. Thus, the trigonometric form is $9\sqrt{2}(\cos\frac{3\pi}{4} + i\sin\frac{3\pi}{4})$.

Find the Trigonometric Form Of −9+9i- 9 + 9 i−9+9i A)

Find the Trigonometric Form Of $- 9 + 9 i$
A)