If a + ib= (c + i)/(c - i ), where c is real, prove that a^2 + b^2 = 1 and b/a = 2c/c^2 - 1

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If (a + ib) = c + i/c - i ,where c is real, Prove that a² + b² = 1 and b/a = 2c/c² - 1 If (a + ib) = c + i/c - i ,where c is real, Prove that a² + b² = 1 and b/a = 2c/c² - 1
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