State whether the following statement is true or false.
If $z - ¯ z = x + i y$ , then $y = 0$

True

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False

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Solution

The correct option is B False
Let $z = a + i b$ .
Hence $¯ z = a - i b$
So, $z - ¯ z = (a + i b) - (a - i b) = i 2 b$ which is purely imaginary.
Hence $x = 0$ and $y = 2 b$ .

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