Given. Z = (| Z | - 1) + 5I, find the complex Z | Math enthusiast | Mathematical art

Given. Z = (| Z | - 1) + 5I, find the complex Z

Let z = x + Yi (x, y ∈ R), ∵ z = (| Z | - 1) + 5I, ∵ x-yi = (x2 + y2-1) + 5I; from the equality of complex numbers, we obtain x = x2 + Y2 − 1 − y = 5, and the solution is x = 12Y = − 5; ∵ z = 12-5i

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