What does the curve from the equation |z+1-i| = 2 look like in the complex plane?

1 Answer
Dec 28, 2015

The curve is a circle of radius #2# centered at #-1+i#.

Explanation:

In general, for any given #z_0 in CC#,
#|z - z_0| = r# is a circle of radius #r# centered at #z_0#.

This should make sense intuitively, as #|z-z_0|# may be interpreted as the distance between #z# and #z_0#. The locus of points a fixed distance from a given point is a circle centered at that point with that distance as the radius.

For the given equation, then

#|z+1-i|=2#

#=> |z - (-1 + i)| = 2#

Thus the curve is a circle of radius #2# centered at #-1+i#.