If the four complex numbers z , z ¯ , z ¯ - 2 Re z ¯ and z - 2 Re z represent the vertices of…

If the four complex numbers z,z¯,z¯-2Rez¯ and z-2Rez represent the vertices of a square of side 4 units in the Argand plane, then z is equal to :
  1. 42
  2. 4
  3. 22
  4. 2

Solution

Let z=x+iy

∴ length of side =4

then z-z¯=4

2iy=4

y=2

also z-z-2Rez=4

2x=4⇒x=2

z=x2+y2=22

Asked in: JEE Main 2020 (05 Sep Shift 1)

Practice more Complex Number questions on Aicharya