Describe the set of all complex numbers that are at a distance of 2 units from the origin.

The set of all complex numbers that are at a distance of 2 units from the origin is

A complex number, written in rectangular form is

The distance of a complex number from the origin (the modulus of the complex number, denoted by ) is given by the formula

Since we want all the complex numbers to be at the distance of 2 units from the origin, they must satisfy

thus, the set we are looking for is

where is the set of all complex numbers

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The description of the set is .

Step-by-step explanation:

From Complex Analysis, we remember that complex numbers are numbers whose form is:

, (1)

Where .

In addition, the distance from the origin is defined by the following Pythagorean identity:

(2)

The following condition must be satisfied:

Then, the set of all complex numbers that are at a distance of 2 units from the origin is described below:

(3)

true

step-by-step explanation: