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If x + i y =(a+i b)/(a-i b),prove that x...

If `x + i y =(a+i b)/(a-i b),`prove that `x^2+y^2=1`.

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To prove that \( x^2 + y^2 = 1 \) given that \( x + iy = \frac{a + ib}{a - ib} \), we will follow these steps: ### Step 1: Express \( z \) in terms of \( a \) and \( b \) Let \( z = x + iy = \frac{a + ib}{a - ib} \). ### Step 2: Multiply by the conjugate of the denominator To simplify \( z \), multiply the numerator and the denominator by the conjugate of the denominator: \[ ...
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