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  • If the four complex numbers  and <img alt="z-2Re(z)" sr

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

Answers (1)

best_answer

Let z = x + iy

Length of side = 4

AB = 4

\\ |z-\bar{z}|=4\\ |2 y|=4 ;|y|=2

BC = 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}

Posted by

himanshu.meshram

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