Turns out, the previous answer I posted was wrong.
Here's the correct solution :-
z2 = 24 - 32i
Let z = x + iy
⇒ z2 = x2 + i2y2 + 2xiy
= x2 - y2 + 2xiy
Now, the real part,
x2 - y2 = 24 ...(1)
Imaginary part,
2xy = -32
xy = -16
x = -16/y
From (1)
x2 - 256/x2 = 24
x4 - 256 = 24x2
x4 - 24x2 - 256 = 0
Solving this equation,
x2 = -8, 36
⇒x = 6
y = -8/3
Thus z = 6 - 8i/3
|z| = √62+(8/3)2
= 6.57
Hope this helps :)