If z, z ,-z,- z forms a rectangle of area 2 3 square units, then one such z is

Step-by-step solution

Let a complex number, z=x+i y z = x -i y Then, vertices of rectangle for z, z ,-z,- z are (x, y),(x,-y),(-x,-y),(-x, y) Now, Area of rectangle =(2 x)(2 y)=4 x y It is given that, Area =2 3 =4 x y 2 x y= 3 x= 1 2 , y= 3 z= 1 2 + 3 i