COMPLEX NUMBERS - NUMBER THEORY
plex number has a square root: THEOREM 5.2.1 If w is a non–zero complex number, then the equation z2 = w has a so-lution z ∈ C. Proof. Let w = a+ib, a, b ∈ R. Case 1. Suppose b = 0. Then if a > 0, z = √ a is a solution, while if a < 0, i √ −a is a solution. Case 2. Suppose b 6= 0. Let z = x + iy, x, y ∈ R. Then the equation z2 = w ...
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