Answer to Question #218562 in Complex Analysis for Unknown346307

Question

If z is a complex number and |z + 16| = 4 |z + l|, find the value of | z|

Answer 1

z=x+yi

|z+16|=4|z+1|

|x+yi+16|²=4²|x+yi+1|²

[(x+16)²+y²]=16[(x+1)²+y²]

x²+32x+256+y²=16x²+32x+16+16y²

15x²+15y²=240

x²+y²=16

|z|=|x+yi|=4