Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary.
-$- 4 + 4 \mathrm { i }$
A) $4 \sqrt { 2 } \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right)$
B) $4 \sqrt { 2 } \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$
C) $16 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$
D) $16 \left( \cos 120 ^ { \circ } + \mathrm { i } \sin 120 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The magnitude of the complex number $-4 + 4i$ is $|z| = \sqrt{(-4)^2 + (4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2}$. The argument $\theta$ can be found using the formula $\tan(\theta) = \frac{y}{x}$, where $x = -4$ and $y = 4$. This gives $\tan(\theta) = -1$, which corresponds to an angle of $135^\circ$ in the second quadrant (since the complex number is in the second quadrant where both sine and cosine are negative and positive, respectively). Therefore, the polar form is $4\sqrt{2}(\cos 135^\circ + i\sin 135^\circ)$.

Write the Complex Number in Polar Form −4+4i- 4 + 4 \mathrm { i }−4+4i

Write the Complex Number in Polar Form $- 4 + 4 \mathrm { i }$