Every non-zero complex number has precisely two square roots: For each complex \(z \neq 0\), the equation \(z = w^{2}\) has two solutions, formally \(w = \pm\sqrt{z}\). If we traverse the unit circle in the \(z\)-plane, however, the "positive" and "negative" square roots are continuouosly exchanged. This image depicts the Riemann surface of the complex square root by projecting away the imaginary part of \(w\).
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