Question

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

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

a +ib = (x +i)² / 2x² +1 ....(i)

= (x²-1+2xi)/(2x² + 1)

and conjugate of a+ib is a-ib

a- ib = (x²- 1-2xi)/(2x²+1)

= (x - i)²/(2x² + 1) ....(ii)

from (i) and (ii) we get,

(a + ib)(a - ib) = a² + b²

= (x² + 1)²/(2x² + 1)²