Find the trigonometric form of the complex number shown below.
-6i
A) $6 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$
B) $6 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$
C) $6 ( \cos 0 + i \sin 0 )$
D) $6 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$
E) $6 ( \cos \pi + i \sin \pi )$

Question

Find the trigonometric form of the complex number shown below. ​
-6i
A)​ $6 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$
B)​ $6 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$
C) $6 ( \cos 0 + i \sin 0 )$
D)​ $6 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$
E)​ $6 ( \cos \pi + i \sin \pi )$

Quizplus · Accepted Answer

The trigonometric form of a complex number is given by $r(\cos \theta + i\sin \theta)$, where $r$ is the magnitude of the complex number and $\theta$ is the argument. For the complex number $-6i$, the magnitude $r = 6$ and the argument $\theta = \frac{3\pi}{2}$, because it lies on the negative imaginary axis. Therefore, the correct trigonometric form is $6 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$.

Find the Trigonometric Form of the Complex Number Shown Below 6(cos⁡π4+isin⁡π4)6 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)6(cos4π​+isin4π​)

Find the Trigonometric Form of the Complex Number Shown Below $6 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$