Question

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

Answer 1

$a + ib = \frac{(x + i) {}^{2} }{(2x {}^{2} + 1) {}^{2} } \\ taking \: rhs \: \\ = \frac{ {x}^{2} + {i}^{2} + 2xi }{4 {x}^{4} + 1 + 4 {x}^{2} } \\ a + ib= \frac{ {x}^{2} - 1}{(2 {x}^{2} + 1) {}^{2} } + i \: \frac{2x}{(2 {x}^{2} + 1) {}^{2} } \\ compare \\ a = \frac{ {x}^{2} - 1 }{(2 {x}^{2} + 1) {}^{2} } \\ b = \frac{2x}{(2 {x}^{2} + 1) {}^{2} } \\ {a}^{2} + {b}^{2} \\ = \frac{( {x}^{2} - 1) {}^{2} }{(2 {x}^{2} + 1) {}^{4} } + \frac{4x {}^{2} }{(2 {x}^{2} + 1) {}^{4} } \\ = \frac{( {x}^{2} + 1) {}^{2} }{(2 {x}^{2} + 1) {}^{4} }$


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Answer 2

Answer:

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