[JEE Main 2013] if z is a complex number of unit modulus and argument theta then arg
If $z$ is a complex number of unit modulus and argument $\theta$, then $\arg\dfrac{1+z}{1+\bar z}$ equals
(a) $-\theta$
(b) $\frac\pi2-\theta$
(c) $\theta$
(d) $\pi-\theta$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 4d ago
▲ 0
Correct answer: (c) $\theta$
$\frac{1+z}{1+\bar z}=\frac{1+z}{\overline{1+z}}$ has argument $2\arg(1+z)$; for $z=e^{i\theta}$, $\arg(1+z)=\frac\theta2$, so the result is $\theta$.
JEE Main 2013 · Complex Numbers — verified solution by the Vidaara Team.
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