Write the complex number in the form a + bi.
-$4 \left( \cos - 135 ^ { \circ } + i \sin - 135 ^ { \circ } \right)$
A) $- 2 \sqrt { 2 } - 2 \sqrt { 2 } i$
B) $- \sqrt { 2 } - \sqrt { 2 } i$
C) $ - \sqrt { 2 } + \sqrt { 2 } i$
D) $- 2 \sqrt { 2 } + 2 \sqrt { 2 } i$

Question

Quizplus · Accepted Answer

The complex number is in polar form $r(\cos \theta + i\sin \theta)$ with $r=4$, $\theta = -135^\circ$. Converting to rectangular form $a + bi$, we use $a = r\cos\theta$ and $b = r\sin\theta$. Thus, $a = 4\cos(-135^\circ) = -2\sqrt{2}$ and $b = 4\sin(-135^\circ) = -2\sqrt{2}$, making the complex number $-2\sqrt{2} - 2\sqrt{2}i$.

Write the Complex Number in the Form a + Bi 4(cos⁡−135∘+isin⁡−135∘)4 \left( \cos - 135 ^ { \circ } + i \sin - 135 ^ { \circ } \right)4(cos−135∘+isin−135∘)

Write the Complex Number in the Form a + Bi $4 \left( \cos - 135 ^ { \circ } + i \sin - 135 ^ { \circ } \right)$