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प्रश्न
If a + ib = `(x + i)^2/(2x^2 + 1)` prove that a2 + b2 = `(x^2 + 1)^2/(2x + 1)^2`
उत्तर
`a + ib = (x + i)^2/(2x^2 + 1) ......(1)`
i के स्थान पर – i रखने से
By replacing i with –i
`a - ib = (x + i)^2/(2x^2 + 1) ......(2)`
समी. (1) और (2) का गुणा करने पर
On multiplying equations (1) and (2)
`(a + ib)(a - ib) = (x + i)^2/(2x^2 + 1) xx (x - i)^2/(2x^2 + 1)`
or `a^2 - i^2b^2 = [(x+i)(x - i)]^2/(2x^2 + 1)^2`
or `a^2 + b^2 = (x^2 - i^2)^2/(2x^2 + 1)^2`
or `a^2 + b^2 = (x^2 + 1)^2/(2x^2 + 1)^2`
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