Question

if z=x+iy, show that the locus of arg (z-1/z-i)=π/6 is a circle, find it's center and radius​

Answer 1

Step-by-step explanation:

Put z=x+iy in arg(

z+2

z−2

)=

6

π

arg(

(x+2)+iy

(x−2)+iy

)=

6

π

⇒arg((x−2)+iy)−arg((x+2)+iy)=

6

π

tan

−1

x−2

y

−tan

−1

x+2

y

=

6

π

⇒tan

−1

⎝

⎜

⎜

⎜

⎛

1+

x

2

−4

y

2

x−2

y

−

x+2

y

⎠

⎟

⎟

⎟

⎞

=

6

π

⇒

x

2

+y

2

−4

xy+2y−xy+2y

=tan

6

π

=

3

1