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If $z=-\bar{z}$, then which one of the following is correct?
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The correct answer is:
real part of $z$ is zero. $[2012-I]$
Let z $=\mathrm{x}+\mathrm{y}$ then $\overline{\mathrm{z}}=\mathrm{x}-\mathrm{iy}$
Now $z=-\bar{z}$
$\Rightarrow(\mathrm{x}+\mathrm{iy})=-(\mathrm{x}-\mathrm{iy}) \Rightarrow \mathrm{x}+\mathrm{iy}=-\mathrm{x}+\mathrm{iy}$
$\Rightarrow 2 \mathrm{x}=0 \Rightarrow \operatorname{Re}(\mathrm{z})=0$
Now $z=-\bar{z}$
$\Rightarrow(\mathrm{x}+\mathrm{iy})=-(\mathrm{x}-\mathrm{iy}) \Rightarrow \mathrm{x}+\mathrm{iy}=-\mathrm{x}+\mathrm{iy}$
$\Rightarrow 2 \mathrm{x}=0 \Rightarrow \operatorname{Re}(\mathrm{z})=0$
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