since x2+y+4i and −3+x2yi are conjugate. So, x2+y+4i=−3−x2yi (x2+y)+4i=(−3)−x2yi Compare both the sides. x2+y‌‌=−3...(1) 4‌‌=−x2y y‌‌=‌
4
−x2
y‌‌=−‌
4
x2
....(2) Substitute the value of y in equation (1) and (2)
x2−‌
4
x2
=−3 x4+3x2−4=0 (x2+4)(x2−1=0) x=±1 Substitute the value of x in equation (2) y=‌
−4
(1)2
y=−4 The value is calculated as, (|x2|+|y2|)‌‌=|x2|+|y2|+2|x||y| ‌‌=(1)2+(−4)2+2(1)(−4) ‌‌=1+16+8 ‌‌=25