in
the form
We
do this by multiplying top and bottom by the complex conjugate of
the denominator, remembering that
The
complex conjugate of
A Level Maths Notes: FP3 – Complex Fractions, Argand Diagrams, Magnitudes, Arguments and Products of Complex Numbers and Polar Forms
Complex Fractions
Typically we have to express a complex fractionin
the formWe
do this by multiplying top and bottom by the complex conjugate of
the denominator, remembering thatThe
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 expressand
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:
