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# Sketch inequalities in the complex plane

Sketch each of the following sets of complex numbers that satisfy the given inequalities:

1. .
2. .
3. .
4. .

1. Letting we have,

This is a disk of radius centered at . The sketch is as follows:

2. Letting we have,

This is the half-plane with negative real part. The sketch is as follows:

3. Letting we have,

This is the half-plane with positive imaginary part. The sketch is as follows:

4. Letting we have,

This is the region outside the disk of radius centered at the point . The sketch is as follows:

1. Reggie Abano says:

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}

2. Reggie Abanol says:

what is the graph of S = {z :|z| ≤ 1} in the complex plane?

3. Anonymous says:

Describe and sketch the set of points in the complex plane satisfying the
inequality: 1 < |z − 2i| ≤ 3.

4. Anonymous says:

Determine and sketch the sets in the complex plane given by
|𝑧 + 1 − 𝑘𝑖| ≤ 3/2

5. Alvin Renteria says:

What if you had to graph this 4 <=|z-1|+|z+1|<=6 on the complex plane?