Write Complex Numbers in Polar Form
-$5 - 5 i$
A) $5 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$
B) $5 \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$
C) $5 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$
D) $5 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$

Question

Quizplus · Accepted Answer

The magnitude of the complex number $5 - 5i$ is $\sqrt{5^2 + (-5)^2} = \sqrt{50} = 5\sqrt{2}$. The angle $\theta$ in radians, measured counter-clockwise from the positive x-axis to the line segment that represents the complex number, is $\frac{7\pi}{4}$ for the given complex number. Therefore, its polar form is $5\sqrt{2}(\cos\frac{7\pi}{4} + i\sin\frac{7\pi}{4})$.

Write Complex Numbers in Polar Form - 5−5i5 - 5 i5−5i

Write Complex Numbers in Polar Form
- $5 - 5 i$