jee-main 2022 Q61

jee-main · India · session2_27jul_shift1 Complex Numbers Argand & Loci Distance and Region Optimization on Loci

Let the minimum value $v _ { 0 }$ of $v = | z | ^ { 2 } + | z - 3 | ^ { 2 } + | z - 6 i | ^ { 2 } , z \in \mathbb { C }$ is attained at $z = z _ { 0 }$. Then $\left| 2 z _ { 0 } ^ { 2 } - \bar { z } _ { 0 } ^ { 3 } + 3 \right| ^ { 2 } + v _ { 0 } ^ { 2 }$ is equal to
(1) 1000
(2) 1024
(3) 1105
(4) 1196

Let the minimum value $v _ { 0 }$ of $v = | z | ^ { 2 } + | z - 3 | ^ { 2 } + | z - 6 i | ^ { 2 } , z \in \mathbb { C }$ is attained at $z = z _ { 0 }$. Then $\left| 2 z _ { 0 } ^ { 2 } - \bar { z } _ { 0 } ^ { 3 } + 3 \right| ^ { 2 } + v _ { 0 } ^ { 2 }$ is equal to\\
(1) 1000\\
(2) 1024\\
(3) 1105\\
(4) 1196

Paper Questions

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