find the complex numbers Z satisfying the equation:- |Z-4| / |Z-8|=1 & |Z-12 | /|Z-8i|=5/3

Putting z = x + iy, we get

Putting x = 6, we have

When x = 6 and y = 8, we have

z = 6 + 8i

When x = 6 and y = 17, we have

z = 6 + 17i

Thus, z 1 = 6 + 8i and z 2 = 6 + 17i are two complex numbers satisfying the given equations.

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