Question

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

Answer 1

Answer:

The description of the set is $A = \{s\in \mathbb{C}|\|s\| = 2\}$.

Step-by-step explanation:

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

$s = a+i\, b$, $a,b \in \mathbb{R}$ (1)

Where $i = \sqrt{-1}$.

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

$\|s\| = \sqrt{a^{2}+b^{2}}$ (2)

The following condition must be satisfied:

$\|s\| = 2$

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

$A = \{s\in \mathbb{C}|\|s\| = 2\}$ (3)