Sketch each of the following sets of complex numbers that satisfy the given inequalities:
-
.
-
.
-
.
-
.
- Letting
we have,
This is a disk of radius
centered at
. The sketch is as follows:
- Letting
we have,
This is the half-plane with negative real part. The sketch is as follows:
- Letting
we have,
This is the half-plane with positive imaginary part. The sketch is as follows:
- Letting
we have,
This is the region outside the disk of radius
centered at the point
. The sketch is as follows:
Sketch the the set of points in the complex plane of the following sets of inequalities and Identify whether the if it is an open or closed set:
1. S = {z :|z| ≤ 1}
2. S = {z : |z| 1}
5. S = {z ∈ C∶1 ≤ |z| ≤ 2}
what is the graph of S = {z :|z| ≤ 1} in the complex plane?
Describe and sketch the set of points in the complex plane satisfying the
inequality: 1 < |z − 2i| ≤ 3.
Determine and sketch the sets in the complex plane given by
|𝑧 + 1 − 𝑘𝑖| ≤ 3/2
What if you had to graph this 4 <=|z-1|+|z+1|<=6 on the complex plane?