RESOURCES > EIS
> COMPLEX NUMBERS > BASICS
If
you are new to electrochemical impedance, or at least new to doing math with
impedance values, here are a couple of simple facts about the arithmetic of
complex numbers. More hints can be found at "Computing
Impedance Values". Bard & Faulkner
has a useful math appendix also.
Before you rush off to write a computer
program to do arithmetic with complex numbers, consult
Numerical Recipes There are tips and
techniques to make things more "computable," i.e.,
how to compute values without crashing your program! See Sec 5.4.
The
symbol i or
j is used to
represent the square root of 1. American electrochemists prefer
j since it is not
confused with current ( i
). 

The
magnitude of a complex number is generally thought of as a positive (real)
number and is the square root of the sum of the squares of the real and
imaginary parts. It is sometimes called the modulus and often shown as
 (a+jb) . 

The
complex conjugate of a complex number simply negates the imaginary
part. 

To
add or subtract two complex numbers, add or subtract the real and imaginary
parts individually. 

To
multiply two complex numbers, multiply all cross terms and then
collect real and imaginary components. Remember that
j^{2}=1. 

To
invert a complex number, multiply top (numerator) and bottom
(denominator) by the complex conjugate of the denominator. The is
the equivalent of multiplying by one (1), so the value is unchanged. 

To
divide one complex number by another, remember that it is the
same as multiplying by the inverse of the denominator, and to
combine the two hints, above. 

