# Complex plane problem

• Oct 19th 2010, 06:28 AM
SyNtHeSiS
Complex plane problem
Sketch {z E C : |z - 1| + |z + 1| = 4}

Attempt:

$|z - 1| + |z + 1| = 4$
$|x + yi - 1| + |x + yi + 1| = 4$
$\sqrt{(x - 1)^2 + y^2} + \sqrt{(x + 1)^2 + y^2} = 4$
$\sqrt{x^2 - 2x + 1 + y^2} + \sqrt{x^2 + 2x + 1 + y^2} = 4$

I tried squaring both sides to get rid of the square root on the LHS, but this made things more complicated. Is there a simpler way?
• Oct 19th 2010, 06:55 AM
Pandevil1990