Addition/Subtraction Example
$ (2 + 3*i) + (23 - 15*i) = (23 + 2) + (3*i - 15*i) = 25 - 12*i $
$ (-3 + \sqrt{-18}) + (7 - \sqrt{-8}) = (-3 + \sqrt{9 \times 2 \times -1}) + (7 - \sqrt{4 \times 2 \times -1}) = (-3 + 3\sqrt{2} \times i) + (7 - 2\sqrt{2} \times i) = 4 + \sqrt{2} \times i $
Division/Multiplication Example
$ \frac{4}{2+3*i} $ = $ \frac{4}{2+3*i}\times\frac{2-3*i}{2-3*i} $ = $ \frac{8-12*i}{4+6*i-6*i-9i^2} $ = $ \frac{8}{13} - \frac{12}{13}\times i $
$ 7*i \times (7 - 3*i) = 49*i - 21*i^2 = 49*i - 21*(-1) = 21 + 49*i $
Conjugate Example
$ 3 + 5*i = 3 - 5*i $
$ 5 - 20*i = 5 + 20*i $
