Write the complex number in rectangular form.
-$4 \operatorname { cis } 135 ^ { \circ }$
A) $4 \sqrt { 2 } - 2 \mathrm { i } \sqrt { 2 }$
B) $2 \sqrt { 2 } - 2 \mathrm { i } \sqrt { 2 }$
C) $4 \sqrt { 3 } + 2 \mathrm { i } \sqrt { 3 }$
D) $- 2 \sqrt { 2 } + 2 \mathrm { i } \sqrt { 2 }$

Question

Quizplus · Accepted Answer

The rectangular form of a complex number in polar form $ r \operatorname{cis} \theta $ is $ r(\cos \theta + i \sin \theta) $. For $ 4 \operatorname{cis} 135^\circ $, $ \cos 135^\circ = -\frac{\sqrt{2}}{2} $ and $ \sin 135^\circ = \frac{\sqrt{2}}{2} $. Thus, the rectangular form is $ 4(-\frac{\sqrt{2}}{2} + i\frac{\sqrt{2}}{2}) = -2\sqrt{2} + 2i\sqrt{2} $.

Write the Complex Number in Rectangular Form 4cis⁡135∘4 \operatorname { cis } 135 ^ { \circ }4cis135∘

Write the Complex Number in Rectangular Form $4 \operatorname { cis } 135 ^ { \circ }$