Find the trigonometric form of the complex number shown below.
$$- 3 - 3 i$$
A) $3 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$
B) $\sqrt { 3 } \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$
C) $9 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$
D) $3 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$
E) $\sqrt { 2 } \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$

Question

Quizplus · Accepted Answer

The magnitude of the complex number $-3 - 3i$ is $\sqrt{(-3)^2 + (-3)^2} = \sqrt{18} = 3\sqrt{2}$. The angle $\theta$ in the polar form can be found from the relation $\tan(\theta) = \frac{y}{x}$, where $x = -3$ and $y = -3$. This gives $\theta = \frac{5\pi}{4}$ (since the complex number is in the third quadrant). Therefore, the trigonometric form is $3\sqrt{2}(\cos\frac{5\pi}{4} + i\sin\frac{5\pi}{4})$.

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

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