Find the quotient and write the result in a+bi form? (16(cos240^\circ+isin240^\circ)) /(8(cos90^\circ+isin90^\circ))

(16(cos240^\circ+isin240^\circ)) /(8(cos90^\circ+isin90^\circ))

1 Answer
Dec 12, 2017

-sqrt(3)+i

Explanation:

They're of the form r*(cos(theta)+isin(theta)), where r is the modulus and theta is the argument.

To divide complex numbers in trig form you divide their moduli and subtract their arguments: 16/8 = 2 and 240^circ -90^circ = 150^circ:

(16(cos240^\circ+isin240^\circ)) /(8(cos90^\circ+isin90^\circ))=

2(cos(150^circ)+isin(150^circ))=

2(-sqrt(3)/2+1/2i)=

-sqrt(3)+i