Write the complex number in rectangular form.
-$10 \operatorname { cis } 135 ^ { \circ }$
A) $10 \sqrt { 2 } - 5 \mathrm { i } \sqrt { 2 }$

B) $5 \sqrt { 2 } - 5 \mathrm { i } \sqrt { 2 }$

C) $10 \sqrt { 3 } + 5 i \sqrt { 3 }$

D) $- 5 \sqrt { 2 } + 5 i \sqrt { 2 }$

Question

Write the complex number in rectangular form.
-$10 \operatorname { cis } 135 ^ { \circ }$
A) $10 \sqrt { 2 } - 5 \mathrm { i } \sqrt { 2 }$

B) $5 \sqrt { 2 } - 5 \mathrm { i } \sqrt { 2 }$

C) $10 \sqrt { 3 } + 5 i \sqrt { 3 }$

D) $- 5 \sqrt { 2 } + 5 i \sqrt { 2 }$

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 $ 10 \operatorname{cis} 135^\circ $, $ \cos 135^\circ = -\frac{\sqrt{2}}{2} $ and $ \sin 135^\circ = \frac{\sqrt{2}}{2} $. Thus, the rectangular form is $ 10(-\frac{\sqrt{2}}{2}) + 10i(\frac{\sqrt{2}}{2}) = -5\sqrt{2} + 5i\sqrt{2} $.

Write the Complex Number in Rectangular Form 10cis⁡135∘10 \operatorname { cis } 135 ^ { \circ }10cis135∘

Write the Complex Number in Rectangular Form $10 \operatorname { cis } 135 ^ { \circ }$