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sqrt(z)
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3-d plot
The complex square root function is inverse to the complex square. If z = w2, then w = sqrt(z) = z1/2. But since the equation z=w2 has two solutions for every complex number w, the complex square root is two-valued. The image above shows the principal part which is defined by restricting the range of arguments of z to the interval [-Pi, Pi]. This leads to a branch cut along the negative real axis.