z=x(1-i)+24(-2+i) , x is a real number.

Question

if z^2 is a negative real number what is x?

Answer 1

z^2 = 1728-48x - 2(x^2-72x+1152)i

So, if z^2 is real,

x^2-72x+1152 = 0
(x-24)(x-48)

Since z^2 < 0, 1728-48x < 0, so x=48