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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.

Perform the following division and write the quotient in trigonometric form. Write-example-1
User Sathish Kumar J
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1 Answer

15 votes
15 votes

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

Let's apply the Complex Arithmetic Rule:


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

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


(\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}}
(-16+2i)/(13)

User Deepika Lalra
by
2.7k points
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