[JEE Advanced 1996] find all non zero complex numbers z satisfying z iz 2
Find all non-zero complex numbers $Z$ satisfying $\bar Z=iZ^2$.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Answer: $Z=i,\ Z=\dfrac{\sqrt3}2-\dfrac i2,\ Z=-\dfrac{\sqrt3}2-\dfrac i2$.
Taking modulus, $|Z|=1$. Writing $Z=e^{i\theta}$: $e^{-i\theta}=e^{i(2\theta+\pi/2)}\Rightarrow 3\theta=-\frac\pi2-2k\pi$, giving $\theta=\frac\pi2,-\frac\pi6,-\frac{5\pi}6$.
JEE Advanced 1996 · Complex Numbers — verified solution by the Vidaara Team.
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