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) $\frac { 5 } { 2 } + \frac { 5 \sqrt { 3 } } { 2 } \mathrm { i }$
B) $\frac { 4 } { 3 } + \frac { 4 \sqrt { 3 } } { 3 } \mathrm { i }$
C) $1 + \sqrt { 3 } \mathrm { i }$
D) $8 + 8 \sqrt { 3 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To find the quotient, first convert both the numerator and denominator into trigonometric form, which they already are. Then, divide their magnitudes and subtract the angles: $$\frac{8}{3}(\cos(90-30) + i\sin(90-30)) = \frac{8}{3}(\cos60 + i\sin60).$$ Converting back to rectangular form gives $\frac{8}{3} \times \frac{1}{2} + \frac{8}{3} \times \frac{\sqrt{3}}{2}i = \frac{4}{3} + \frac{4\sqrt{3}}{3}i.$

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 $\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }$