if a+ib =( (x+i)2) / (2x2 + 1) prove that a2 +b2 =((x2 + 1)2) / (2x2 +1)2 - Maths - Complex Numbers and Quadratic Equations

Question

if a+ib =( (x+i)2) / (2x2 + 1)
prove that a2 +b2 =((x2 + 1)2)
/ (2x2 +1)2

Manbar Singh · Accepted Answer

We have,a + ib = x+i22x2 + 1   
1Replacing i by -i, we geta-ib = x-i22x2+1    
2multiply 1and 2, we geta+iba-ib = x+i22x2 + 1 ×x-i22x2+1⇒a2 - i2b2 = x2-i222x2+12 ⇒a2 + b2 =x2+122x2+12