Complex number basics and examples
Background and Form
Complex numbers are written in the form $ a+bi $, where a is the "real" part of the number and b is the "imaginary" part. The variable that denotes the imaginary part of the complex number is $ i $, where
$ i=\sqrt{-1} $ and $ \,\!i^2=-1 $
The real part of the number is thought of as lying on the x axis, while the imaginary lies on the y axis, so $ \,\!a+bi $ can also be graphed as a vector. This has special pertinence to Euler's formula, which relates sinusoidal and exponential equations using the complex number plane, but this is outside our scope.
Adding
Complex numbers are added by separating their real and imaginary parts, and adding them separately. The general case is:
$ \,\!(a+bi)+(c+di)=(a+c)+i(b+d) $
