Graphing a complex inequality

Homework Statement

Graph the inequality: |z-1|<|z| where z=x+iy {i is the imaginary number: (-1)^.5}

Homework Equations

for complex #'s z and w,
|w+z|<or=|w|+|z|
|z-w|>or=|z|-|w|

The Attempt at a Solution

|z|-|1|<or=|z-1|<|z| { if we consider 1 to be complex i.e 1=1+0i}
=>|z|-1<|z|
=>-1<0

I have no idea how to graph this last inequality. Isn't it just a true statement in general?

gabbagabbahey
Homework Helper
Gold Member

Homework Equations

for complex #'s z and w,
|w+z|<or=|w|+|z|
|z-w|>or=|z|-|w|

Huh? What do these inequalities (which are always true) have to do with the inequality in the question?

Instead, use $z=x+iy$ to calculate both $|z|$ and $|z-1|$ in terms of x and y and then substitute your results into the given inequality.

HallsofIvy