Given that the complex Z satisfies z-2|z| = - 7 + 4I, find the complex Z
Let z = x + Yi (x, y ∈ R), then x + yi-2 √ (x ^ 2 + y ^ 2) = - 7 + 4I
‖ X-2 √ (x ^ 2 + y ^ 2) = - 7 and y = 4
∴ x^2+14x+49=4x^2+64
3x^2-14x+15=0
The solution is X1 = 3, X2 = 5 / 3
Ψ z = 3 + 4I or Z = 5 / 3 + 4I
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