## Complex Fractions, Argand Diagrams, Magnitudes, Arguments and Products of Complex Numbers and Polar Forms

Complex Fractions

Typically we have to express a complex fraction in the form We do this by multiplying top and bottom by the complex conjugate of the denominator, remembering that The complex conjugate of Example: Express in the form   Argand Diagrams

We may also have to plot complex numbers on an Argand diagram. This is a normal set of axes: is plotted as the point In the diagram below the complex number s plotted as the point  Magnitudes, Arguments and the Polar Form of Complex Numbers

The magnitude of the argument of The polar form of is written as Multiplying Complex Numbers

Given two complex numbers and we can find the product We can express this in polar form as above,  then Or we can express and in polar form then using the normal rules for multiplying exponentials:   so  Dividing Complex numbers

We can use the method of the top of the page to express in cartesian form, or, if we require polar form, using the normal rule for dividing exponentials:  