Question

let z be a complex number such that |z-i/z-2i| = 1 and |z| = 5/2.
then the value of |z+3i| :​

Answer 1

Answer:

Given

∣

∣

∣

∣

∣

z+2i

z−i

∣

∣

∣

∣

∣

=1

⇒∣z−i∣=∣z+2i∣

Let z=x+iy

So, x

2

+(y−1)

2

=x

2

+(y+2)

2

−2y+1=4y+4

6y=−3⇒y=

2

−1

x

2

+y

2

=

4

25

⇒x

2

=

4

24

=6

z=±

6

−

2

i

∣z+3i∣=

6+

4

25

=

4

49

=

2

7

∴

∣2+3i∣=

2

7