[JEE Main 2004] if z x iy and z 1 3 p iq then 1 p 2
If $z=x-iy$ and $z^{1/3}=p+iq$, then $\dfrac{1}{p^2+q^2}\left(\dfrac xp+\dfrac yq\right)$ equals
(a) $-2$
(b) $-1$
(c) $2$
(d) $1$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Correct answer: (a) $-2$
$z=(p+iq)^3$ gives $x=p^3-3pq^2,\ y=q^3-3p^2q$, so $\frac xp+\frac yq=-2(p^2+q^2)$; dividing gives $-2$.
JEE Main 2004 · Complex Numbers — verified solution by the Vidaara Team.
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