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.
Plot the following complex numbers on an Argand Diagram.
a) –5 + 4i
c) 5 – i
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 + 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 .
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