Question

the square root of 3-4i is
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Answer 1

A square root a+i b must satisfy (a+ib)^2 = 3-4i. Now (a+i b)^2 = a^2 -b^2 + 2 a b i. So we want a^2-b^2 = 3 and 2 a b = -4 thats a b = -2.