jee-main 2020 Q52

jee-main · India · session2_05sep_shift1 Complex Numbers Argand & Loci Geometric Properties of Triangles/Polygons from Affixes

If the four complex numbers $z , \bar { z } , \bar { z } - 2 \operatorname { Re } ( \bar { z } )$ and $z - 2 \operatorname { Re } ( z )$ represent the vertices of a square of side 4 units in the Argand plane, then $| z |$ is equal to :
(1) $4 \sqrt { 2 }$
(2) 4
(3) $2 \sqrt { 2 }$
(4) 2

If the four complex numbers $z , \bar { z } , \bar { z } - 2 \operatorname { Re } ( \bar { z } )$ and $z - 2 \operatorname { Re } ( z )$ represent the vertices of a square of side 4 units in the Argand plane, then $| z |$ is equal to :\\
(1) $4 \sqrt { 2 }$\\
(2) 4\\
(3) $2 \sqrt { 2 }$\\
(4) 2

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