loci in the complex plane

Question 1

/z-(a +bi)/

Answer 1

distance from z to the point a + bi

Question 2

A set of points of the form arg (z – z1) = θ

Answer 2

a half line

Question 3

All sets of points of the form arg(z-(a+bi)) = θ consist of

Answer 3

a half-line from the point a + bi in the direction θ.

Question 4

Sets of points of the form θ1 < arg(z - (a + bi)) < θ2 consist of

Answer 4

consist of the two half-lines arg(z-(a+bi)) = θ 1 and arg(z- (a+bi)) = θ2 and the region between them.

Question 5

A locus of the form /z - z1/ = /z - z2/ represents a straight line

Answer 5

basically a line between two points, and the perpendicular bisector between the two

< means z is closer to z1 than z2