JEE Mains Model Paper 4

Since z = x + iy lies in the third quadrant, we get
x < 0 and y < 0
Now,

− z

z

=

x−iy

x+iy

=

(x−iy)(x−iy)

(x+iy)(x−iy)

=

x2−y2−2ixy

x2+y2

=

x2−y2

x2+y2

-

2ixy

x2+y2

Since

− z

z

also lies in third quadrant we get

x2−y2

x2+y2

< 0 and

−2xy

x2+y2

< 0
x2−y2 < 0 and -2xy < 0
x2 < y2 and xy > 0
But x , y < 0
y < x < 0