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Need help This practice asks to fill in the four boxes in the picture

Need help This practice asks to fill in the four boxes in the picture-example-1

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Solution

Find the fourth root of the complex root


2√(3)-2i

Let


\begin{gathered} 2√(3)-2i=r(cos\theta+isin\theta) \\ 2√(3)=rcos\theta.........(1) \\ -2=rsin\theta............(11) \end{gathered}

Squaring + adding the equations


\begin{gathered} r^2(cos^2\theta+sin^2\theta)=-2^2+(2√(3))^2 \\ r^2=4+12 \\ r^2=16 \\ r=√(16) \\ r=4 \end{gathered}
2√(3)-2i=2(cos(2\pi)/(3)+isin(2\pi)/(3))

Need help This practice asks to fill in the four boxes in the picture-example-1
User Sambi Reddy
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