Convert a Complex Number from Polar to Rectangular Form
-$9 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)$
A) $\frac { - 9 \sqrt { 2 } } { 2 } + \frac { 9 \sqrt { 2 } } { 2 } i$
B) $\frac { 9 \sqrt { 2 } } { 2 } + \frac { - 9 \sqrt { 2 } } { 2 } \mathrm { i }$
C) $\frac { 9 \sqrt { 2 } } { 2 } + \frac { 9 \sqrt { 2 } } { 2 } \mathrm { i }$
D) $\frac { - 9 \sqrt { 2 } } { 2 } + \frac { - 9 \sqrt { 2 } } { 2 } \mathrm { i }$

Question

Quizplus · Accepted Answer

The polar form $9(\cos\frac{3\pi}{4} + i\sin\frac{3\pi}{4})$ converts to rectangular form using $\cos\frac{3\pi}{4} = -\frac{\sqrt{2}}{2}$ and $\sin\frac{3\pi}{4} = \frac{\sqrt{2}}{2}$, resulting in $\frac{-9\sqrt{2}}{2} + \frac{9\sqrt{2}}{2}i$.

Convert a Complex Number from Polar to Rectangular Form - 9(cos⁡3π4+isin⁡3π4)9 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)9(cos43π​+isin43π​)

Convert a Complex Number from Polar to Rectangular Form
- $9 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)$