+0

# Complex numbers

0
5
1
+1479

We can represent complex numbers geometrically by plotting them on the "complex plane", just like we plot points on the Cartesian plane.  The real part of the complex number is the horizontal coordinate and the imaginary part is the vertical coordinate.  So, the complex number \$0\$ is the origin.  The number \$2-3i\$ is plotted below.

We say that the magnitude of a complex number is the distance from that complex number to the origin in the complex plane.  We denote the magnitude of the complex number \$a+bi\$ as \$|a+bi|\$.

Compute \$|0 + 2i|\$

Dec 19, 2023

#1
+222
+1

In the complex plane, the point 0+2i corresponds to a point two units vertically above the origin.

Therefore, the magnitude of 0+2i, which represents the distance from this point to the origin, is simply the length of the vertical segment connecting the two points.

Since this segment has length 2, the magnitude of 0+2i is also 2.

So, the answer is:

|0 + 2i| = -2

Dec 19, 2023

#1
+222
+1

In the complex plane, the point 0+2i corresponds to a point two units vertically above the origin.

Therefore, the magnitude of 0+2i, which represents the distance from this point to the origin, is simply the length of the vertical segment connecting the two points.

Since this segment has length 2, the magnitude of 0+2i is also 2.

So, the answer is:

|0 + 2i| = -2

BuiIderBoi Dec 19, 2023