Find the trigonometric form of the complex number shown below. $- 3 i$
A) $3 ( \cos 0 + i \sin 0 )$
B) $3 ( \cos \pi + i \sin \pi )$
C) $3 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$
D) $3 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$
E) $3 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$

Question

Quizplus · Accepted Answer

The complex number $-3i$ has a magnitude of 3 and an angle of $-\frac{\pi}{2}$ (measured counterclockwise from the positive real axis). Using the definitions of cosine and sine in the unit circle, we have $\cos \left(-\frac{\pi}{2}\right) = 0$ and $\sin \left(-\frac{\pi}{2}\right) = -1$. Thus, the complex number can be written in trigonometric form as $3\left(\cos\frac{3\pi}{2} + i\sin\frac{3\pi}{2}\right)$. Option C matches this form.

Find the Trigonometric Form of the Complex Number Shown Below −3i- 3 i−3i

Find the Trigonometric Form of the Complex Number Shown Below $- 3 i$