if z = x+iy and z^2 = a+ib where a,b,x,y are real numbers, show that 2x^2 = √a^2+b^2 + a - Maths - Complex Numbers and Quadratic Equations

Question

if z = x+iy and z^2 = a+ib where a,b,x,y are real numbers, show
that 2x^2 = √a^2+b^2 + a

Anuradha Sharma · Accepted Answer

z2= a+ib x+iy2=  a+ib x2-y2+2ixy =   a+ib Comparing, we get x2-y2= a 
12xy = b x2+y2= x2-y22+4x2y2= a2+b2
2Adding equation 1 and 2, 2x2= a+a2+b2