Question

Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the argument in radians and round it to twodecimal places if necessary.

Answer 1

$\text{ }\frac{-4\text{ - 2i }}{\text{ 3 + 2i}}$

Let's apply the Complex Arithmetic Rule:

$\frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}\:=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}$

We have: a = -4, b = -2, c = 3 & d = 2

$\frac{\left(-4\cdot \:3+\left(-2\right)\cdot \:2\right)+\left(-2\cdot \:3-\left(-4\right)\cdot \:2\right)i}{3^2+2^2}$$\frac{(-12\text{ - 4\rparen + \lparen-6 + 8\rparen i}}{9\text{ + 4}}$$\frac{-16+2i}{13}$