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Question Corner -- What is the Square Root of i?
https://www.math.toronto.edu/mathnet/questionCorner/rootofi.html
May 9, 1997 - The equation means . However, if you plug a=-b into the second equation you get which can not be satisfied by any real number b. ... However, the easiest and most insightful way to take the square root of a complex number (as well as any higher order roots) is to use the geometric representation of the complex numbers.How can you find the complex roots of i? - Mathematics Stack Exchange
https://math.stackexchange.com/questions/.../how-can-you-find-the-complex-roots-of...
Sep 30, 2010 - If the polar form of z is z=r(cosθ+isinθ),. there are n distinct solutions to the equation wn=z: w=n√r(cosθ+2πkn+isinθ+2πkn),. where k=0,1,...
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