Can we prove by taking modulus on both the sides 11 If a+ib = - Maths - Complex Numbers and Quadratic Equations

Question

Can we prove by taking modulus on both the sides?

11       I f   a + i b   =   x + i 2
2 x 2 + 1 ,   p r o v e   t h a t   a 2   +
  b 2   =   x 2 + 1 2 2 x 2   +   1 2

Aarushi Mishra · Accepted Answer

Dear student
Yes you can take modulus on both sides and use its properties

a+ib=x+i22x2+1a+ib=x+i22x2+1a+ib2=x+i22x2+12a+ib2=x+i42x2+12=x+i42x2+12a2+b2=x2+142x2+12a2+b2=x2+122x2+12

Can we prove by taking modulus on both the sides? 11 . I f a + i b = x + i 2 2 x 2 + 1 , p r o v e t h a t a 2 + b 2 = x 2 + 1 2 2 x 2 + 1 2 .