Find the complex Z satisfying the following conditions (1) Absolute value Z-Z = 10-1-2i (2) z^2=7+24i The z-handle of (1) is a conjugate complex number. I'm sorry

Find the complex Z satisfying the following conditions (1) Absolute value Z-Z = 10-1-2i (2) z^2=7+24i The z-handle of (1) is a conjugate complex number. I'm sorry

Absolute value z-z-z = absolute value Z-Z = 10-1-2i = 10 (1 + 2I) / [(1-2i) (1 + 2I)] = 2 + 4I
Solve the above equation
Z = a + bi
b=4
Root sign (a + b) + a = 2
a=-3
Z = - 3 + 4I
z=-3-4i
z^2=7+24i
=7+2*12i
=16-9i^2+2*4*3i
=(4-3i)^2
z=+-(4-3i)