Complex Numbers

Definition

$C$, set of complex numbers is the set of numbers in the form of $a+bi$.

Recall that $i^2=-1$

Therefore,

$$(a+bi)(c+di)=ac+adi+bci+bd{i}^2$$ $$(a+bi)(c+di)=(ac-bd)+(ad+bc)i$$

but the summation is much more straight forward:

$$(a+bi)+(c+di)=(a+c)+(b+d)i$$