Question

|If z is a complex number and |z+16| = 4|z+1|, find the value of |z|

Answer 1

Let z=x+iy, then,
\(\sqrt{(x+16)^2 +y^2}=4\sqrt{(x+1)^2+y^2}\)
it can be deduced that it is a circle

Answer 2

It's asking for the value of |z|

Answer 3

there is no 1 defind value. It is all the values that lie on this circle

Answer 4

The answer is |z| = 4, apparently

Answer 5

it's a circle centered at origin qith radius =4

Answer 6

squaring bouth sides:
(x+16)^2+y^2=16[(x+1)^2+y^2]
x^2+32x+16^2+y^2=16x^2+32x+16+16y^2
16^2-16=16x^2-x^2+16y^2-y^2
16(16-1)=x^2(16-1)+y^2(16-1)
16=x^2+y^2
this is equation of circle centered at origin with radius 4. In coplex plane you can write it like |z|=4