If the four complex numbers


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

  2. 2

  3. $4 \sqrt{2}$

  4. $2 \sqrt{2}$

Correct Option: , 4


Let $z=x+i y$

Length of side $=4$



$|2 y|=4 ;|y|=2$

$B C=4$

$\mid \bar{z}-(\bar{z}-2 \operatorname{Re}(\bar{z}) \mid=4$

$|2 x|=4 ;|x|=2$

$|z|=\sqrt{x^{2}+y^{2}}=\sqrt{4+4}=2 \sqrt{2}$

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