JEE PYQ: Complex Numbers Question 20
Question 20 - 2020 (05 Sep Shift 1)
If the four complex numbers $z$, $\bar{z}$, $\bar{z} - 2\text{Re}(\bar{z})$ and $z - 2\text{Re}(z)$ 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) $2$
Show Answer
Answer: (3)
Solution
Let $z = x + iy$. Then vertices: $(x,y)$, $(x,-y)$, $(-x,-y)$, $(-x,y)$. Side $= 2|x| = 4$ or $2|y| = 4$. So $|x| = 2, |y| = 2$. $|z| = \sqrt{4+4} = 2\sqrt{2}$.
BETA
