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Goryan [66]
1 year ago
15

Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the argume

nt in radians and round it to twodecimal places if necessary.

Mathematics
1 answer:
Tema [17]1 year ago
3 0
\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}

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