Definition
A complex number is made up of two parts, a real part and an imaginary part. An example is
$ a+bi $, where $ a $ is the real part and $ b $ is the imaginary part.
Addition
$ (a + bj) + (c + dj) = (a + c) + (b + d)j $
Subtraction
$ (a + bj) - (c + dj) = (a - c) + (b - d)j $
Multiplication
$ (a + bj)(c + dj) = (ac - bd) + (ad + bc)j $
Division
$ \frac{(a + bj)}{(c + dj)} = \frac{(a + bj)(c - dj)}{(c + dj)(c - dj)} = \frac{(a + bj)(c - dj)}{(c^2 - d^2)} = \frac{(ac + bd) + (bc - ad)j}{(c^2 - d^2)} $
Applications
Applications include:
- Control Theory
- Fluid Flow
- Signal Processing
- Quantum Mechanics
- Relativity
- Fractals (my personal favorite)
