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www.math.toronto.edu/mathnet/questionCorner/rootofi.html

Note however that when taking the square root of a complex number it is also important to consider these other representations. For instance, i can also be viewed as being 450 degrees from the origin. Using this angle we find that the number 1 unit away from the origin and 225 degrees from the real axis () is also a square root of i.

en.wikipedia.org/wiki/Imaginary_unit

The term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root.

www.milefoot.com/math/complex/squarerootofi.htm

Therefore, the square root of $-5+12i$ is $2+3i$. So now we have demonstrated one case where the square root of a complex number is another complex number. An algebraic derivation

www.youtube.com/watch?v=HhlD7sX5Tp8

Finding roots of complex numbers. Here I give the formula to find the n-th root of a complex number and use it to find the square roots of a number. Category

math.stackexchange.com/questions/44406

The square root is not a well defined function on complex numbers. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number.

en.wikipedia.org/wiki/Square_root

The square of any positive or negative number is positive, and the square of 0 is 0. Therefore, no negative number can have a real square root. However, it is possible to work with a more inclusive set of numbers, called the complex numbers, that does contain solutions to the square root of a negative number.This is done by introducing a new number, denoted by i (sometimes j, especially in the ...

www.algebra.com/algebra/homework/complex/How-to-take-a-square-root-of-a...

How to take a square root of a complex number Taking a root of a complex number was just considered in the lesson How to take a root of a complex number in this module. In that lesson the original complex numbers were presented in the trigonometric form

www.intmath.com/complex-numbers/7-powers-roots-demoivre.php

Powers and Roots of Complex Numbers. by M. Bourne. Consider the following example, which follows from basic algebra: ... the power 'n' is a half because of the square root and the terms inside the square root can be simplified to a complex number in polar form.

www.qc.edu.hk/math/Advanced Level/Finding the square root of a complex number.htm

Find the square root of a complex number . Question Find the square root of 8 – 6i. First method Let z 2 = (x + yi) 2 = 8 – 6i \ (x 2 – y 2) + 2xyi = 8 – 6i Compare real parts and imaginary parts,

www.symbolab.com/solver/complex-numbers-calculator

Free Complex Numbers Calculator - Simplify complex expressions using algebraic rules step-by-step