JEE Main 2013 (Online) 25th AprilQuestion 1
Let $z$ satisfy $|z|=1$ and $z=1-\bar z$.
Statement 1 : $z$ is a real number.
Statement 2 : Principal argument of $z$ is $\frac\pi3$.
Complex Numbers
Solution
$z+\bar z=1$ and $|z|=1$ give $z=\frac12\pm\frac{\sqrt3}2i$, not real, so Statement 1 is false; the principal argument is $\pm\frac\pi3$, so Statement 2 is taken as true.