Complex Numbers Continued - The Argand Diagram

 

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 + bi 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?

 

Modulus

 

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 + bi, 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