Let z=x+iy Then, we have z+|z|=8+12i ⇒‌‌(x+iy)+|x+iy|=8+12i ⇒‌‌(x+√x2+y2)+iy=8+12i On comparing the real and imaginary part, we get y=12 and x+√x2+y2=8 ⇒‌‌√x2+144=8−x On squaring both sides, we get x2+144=64+x2−16x ⇒‌‌16x=−80 ⇒‌‌x=−5 ∴‌‌z=x+iy=−5+i⋅12 Then, |z|=√25+144=√169=13 ⇒‌‌|z|2=169 ⇒‌‌|z2|=169  (∵|zn|=|z|n)