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 is $\sqrt{(-3)^2 + (-3)^2} = 3\sqrt{2}$, and its angle with the positive x-axis is $\frac{5\pi}{4}$ because it lies in the third quadrant where both x and y are negative.

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 $- 3 - 3 i$