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use the polar form of the complex number to find a value in Cartesian form, z = x + iy.

 

sqrt(-i)

 Mar 17, 2019
edited by Guest  Mar 18, 2019
 #1
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\(z = r e^{i \theta}\\ \sqrt{z} = \sqrt{r} e^{i \theta/2}\\ -i = 1\cdot e^{-i \pi /2}\\ \sqrt{-i} = \sqrt{1} e^{-i \pi/4} = e^{-i\pi/4} = \\ \cos(-\pi/4) + i \sin(-\pi/4) = \\ \dfrac{\sqrt{2}}{2}(1 - i)\)

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 Mar 18, 2019
 #2
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Thanks :D. Really helpful. I didn't realize that you should sqrt the equation to find out the equation for a rooted complex number :D

Guest Mar 19, 2019

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