Here are the basic arithmetic operations performed on complex numbers. These are something that should come as second nature to anyone at this level.
- Addition - $ \,(a + bi) + (c + di) = (a + c) + (b + d)i\, $
- Subtraction - $ \,(a + bi) - (c + di) = (a - c) + (b - d)i\, $
- Multiplication - $ \,(a + bi)(c + di) = (ac - bd) + (bc + ad)i\, $
- Division - $ \,\frac{(a + bi)}{(c + di)} = \frac{(ac + bd)}{(c^2 + d^2)} + \frac{(bc - ad)}{(c^2 + d^2)}i\, $
