Complex Numbers

x+iy=

1

a+ibt

x+iy=

a−ibt

a2+b2t2

Let a≠0‌&‌b≠0
x=

a

a2+b2t2

...............(1)
y=

−bt

a2+b2t2

...............(2)

y

x

=

−bt

a

⇒t=−

ay

bx

put in (1)
x{a2+b2.

a2y2

b2x2

}=a
x2+y2−

1

a

x=0
(x−

1

2a

)2+y2=

1

4a2

⇒ option A is correct
for a ≠ 0,b = 0
x+iy=

1

a

x=

1

a

,y=0⇒z lies on x-axis ⇒ option (C) i correct
for a = 0,b ≠ 0
x+iy=

1

ibt

y=−

1

b

ti,x=0
⇒ z lies on y-axis. ⇒ option (D) is correct