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 A True
Let $z = a + i b$ .

Hence $¯ z = a - i b$

So, $z + ¯ z = (a + i b) + (a - i b) = 2 a$ which is purely real.

Hence $x = 2 a$ and $y = 0$ .

Suggest Corrections

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