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If (a + ib) = (1 + i)/(1 - i), then prove that a^2 + b^2 = 1.

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If (a + ib) = (1 + i)/(1 - i), then prove that a2 + b2 = 1.

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∴ a + bi = 0 + i

Equating real and imaginary parts, we get

a = 0 and b = 1

a2 + b2 = 02 + 12 = 1

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