if ( p+iq)2= x+iy, prove that (p2+q2)2=x2+y2 - Maths - Complex Numbers and Quadratic Equations

Question

if ( p+iq)2= x+iy, prove that (p2+q2)2=x2+y2

Garre Venkata Saisharan · Answer

(p+iq)2=x+iy => p2-q2+2ipq=x+iy
=> x=p2-q2 ; y=2pq
R H S => x2+y2=( p2-q2)2+(2pq)2
=p4+q4-2p2q2+4p2q2
=p4+q4+2p2q2
=(p2+q2)2