An Argand Diagram is used to make a pictorial representation
of a complex number. The horizontal
axis is called the real axis and is used to plot the real (a) part of a complex
number. The vertical axis becomes the
imaginary axis and is used to plot the imaginary (b) part of a complex
number. The complex number a + b*i*
is plotted as a point that has coordinates (a, b) on the Argand Diagram.

**Sample Questions:**

Plot the following complex numbers on an Argand Diagram.

a) –5 + 4i

b) -3

c) 5 – i

d) 2i

e) 4 + 5i

f) –2 – 4i

Take a look at the point you’ve plotted. What is true of all points on the real axis? What is true of all points on the Imaginary axis?

The absolute value of a real number is equal to the distance
between 0 and x on a real number line.
The absolute value of a complex number, z = a + b*i*, is called its
modulus and is written |z|. It is equal
to the distance between the origin and the point z in the complex plane. This is the length of the vector from the
origin to the point z. According to the
distance formula _{}.

Practice Problems:

p281 #42, 43