jee-main 2023 Q62

jee-main · India · session2_12apr_shift1 Complex Numbers Argand & Loci Distance and Region Optimization on Loci
Let $C$ be the circle in the complex plane with centre $z _ { 0 } = \frac { 1 } { 2 } ( 1 + 3 i )$ and radius $r = 1$. Let $z _ { 1 } = 1 + i$ and the complex number $z _ { 2 }$ be outside circle $C$ such that $\left| z _ { 1 } - z _ { 0 } \right| \left| z _ { 2 } - z _ { 0 } \right| = 1$. If $z _ { 0 } , z _ { 1 }$ and $z _ { 2 }$ are collinear, then the smaller value of $\left| z _ { 2 } \right| ^ { 2 }$ is equal to
(1) $\frac { 5 } { 2 }$
(2) $\frac { 7 } { 2 }$
(3) $\frac { 13 } { 2 }$
(4) $\frac { 3 } { 2 }$
Let $C$ be the circle in the complex plane with centre $z _ { 0 } = \frac { 1 } { 2 } ( 1 + 3 i )$ and radius $r = 1$. Let $z _ { 1 } = 1 + i$ and the complex number $z _ { 2 }$ be outside circle $C$ such that $\left| z _ { 1 } - z _ { 0 } \right| \left| z _ { 2 } - z _ { 0 } \right| = 1$. If $z _ { 0 } , z _ { 1 }$ and $z _ { 2 }$ are collinear, then the smaller value of $\left| z _ { 2 } \right| ^ { 2 }$ is equal to\\
(1) $\frac { 5 } { 2 }$\\
(2) $\frac { 7 } { 2 }$\\
(3) $\frac { 13 } { 2 }$\\
(4) $\frac { 3 } { 2 }$