Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }$$
A) $\frac { 4 } { 3 } + \frac { 4 \sqrt { 3 } } { 3 }$ i
B) $\frac { 5 } { 2 } + \frac { 5 \sqrt { 3 } } { 2 } \mathrm { i }$
C) $8 + 8 \sqrt { 3 } i$
D) $1 + \sqrt { 3 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers in trigonometric form, divide the magnitudes and subtract the angles. Here, the magnitude of the numerator is 8 and its angle is 90 degrees. The magnitude of the denominator is 3 and its angle is 30 degrees. The quotient's magnitude is $8/3$ and its angle is $90 - 30 = 60$ degrees. Converting back to rectangular form using $\cos 60 = 1/2$ and $\sin 60 = \sqrt{3}/2$, the quotient is $\frac{8}{3}(\frac{1}{2} + \frac{\sqrt{3}}{2}i) = \frac{4}{3} + \frac{4\sqrt{3}}{3}i$.

Find the Quotient and Write in Rectangular Form 8(cos⁡90+isin⁡90)3(cos⁡30+isin⁡30)\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }3(cos30+isin30)8(cos90+isin90)​

Find the Quotient and Write in Rectangular Form $\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }$