[JEE Advanced 1982] if z sqrt 3 2 i2 5 sqrt 3 2 i2 5 then
If $z=\left(\frac{\sqrt3}2+\frac i2\right)^5+\left(\frac{\sqrt3}2-\frac i2\right)^5$, then
(a) $\operatorname{Re}(z)=0$
(b) $\operatorname{Im}(z)=0$
(c) $\operatorname{Re}(z)>0,\operatorname{Im}(z)>0$
(d) $\operatorname{Re}(z)>0,\operatorname{Im}(z)<0$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Correct answer: (b) $\operatorname{Im}(z)=0$
$\frac{\sqrt3}2\pm\frac i2=e^{\pm i\pi/6}$, so $z=2\cos\frac{5\pi}6=-\sqrt3$, which is real: $\operatorname{Im}(z)=0$.
JEE Advanced 1982 · Complex Numbers — verified solution by the Vidaara Team.
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