Question

if |z| = 2 then find the locus of complex number (a+ bz)

Answer 1

|a+bz|=b|ab+z|

if |z|=2
the |ab+z|=2

centre of circle shifted from 0,0 to (-ab,0)

thus
|a+bz|=2b
thus it is a circle 

Answer 2

Step-by-step explanation:

|a+bz|=b|ab+z|

if |z|=2

the |ab+z|=2

centre of circle shifted from 0,0 to (-ab,0)

thus

|a+bz|=2b

thus it is a circle