+0

# Complex numbers

0
25
2
+1733

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 \$|1| |2i| |3| |i|\$.

Jan 10, 2024

#1
+16
+1

Basically, we're trying to find the distance between (1, 0) (0, 0) x the distance between (2, 1) (0, 0) x the distance between (3, 0) (0, 0) x the distance between (0, 1) (0, 0)

By using the distance formula, we can find

distance between (1, 0) (0, 0) = 1

distance between (2, 1) (0, 0) = √3

distance between (3, 0) (0, 0) = √5

distance between (0, 1) (0, 0) = 1

\$|1| |2i| |3| |i|\$ = 1 x √3 x √5 x 1 = √3 x √5 = √15

Jan 11, 2024