Geometric reps of complex formula

[wildman]

Homework Statement

Describe geometrically the sets of points determined by the relations:

a) |z-i|+|z-1| = 2
b) |z-i|=|z+1|
c) Re z = |z-2|

Homework Equations

The Attempt at a Solution

I know the answer of a is suppose to be Ellipse with foci at i and 1, major axis 2
and b is Perpendicular bisector of the line segment connecting z=i and z = -1
and c is Parabola focus at z=2, directrix the imaginary axis (from the back of the book), but could one of you help me to see how the author got those answers?

 

[Dick]

The most direct way to handle all of them is to put z=x+iy and look at the x,y equations. You could also look up the geometric definition of an ellipse and a parabola to do those more directly.

 

[wildman]

Yep. The direct method worked. Thanks.