Question

Find the Cartesian inequation for the region represented by |z+8|<|z-6| ... Could anyone please perhaps help me with this??

Answer 1

This was my working, and it was wrong....
Let z=x+iy
:. z+8=(x+8)+iy
z-6=(x-6)+iy
and so
|z+8|=sqrt[(x+8)^2 + y^2]
|z-6|=sqrt[(x-6)^2 +y^2]
goes to
(x+8)^2 + y^2 < (x-6)^2 + y^2
(x+8)(x+8) < (x-6)(x-6)
which simplifies to
18x < -28
x < -14/9

What have I done incorrectly?

Answer 2

(x+8)^2 < (x-6)^2

x^2 +16x +64 < x^2 -12x +36

28x < -28

x < -1

Answer 3

Oh wow thats annoying hahaha I've been looking at this for ages! Cheers

Answer 4

:)