Suppose z e C (z is an element of the complex numbers) Let z = x + yi with x,y e R. Let (z) = x - yi with x,y e R. Prove: (z) = z if and only if z is a real number. I'm having trouble with this proof in both directions. Thanks for any help.
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Originally Posted by jzellt Suppose z e C (z is an element of the complex numbers) Let z = x + yi with x,y e R. Let (z) = x - yi with x,y e R. Prove: (z) = z if and only if z is a real number. I'm having trouble with this proof in both directions. Thanks for any help. If z is real then y = 0 and it is trivially seen that z = (z). If (z) = z then x = x and y = -y => y = 0 => z is real.
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