Arithmetic has distinct rules when it involves complex numbers. In the case of addition, our definition is (a + bi) + (c +di) = (a + c) + (b +d)i.Don't be intimidated by the new concept of a complex number. The rules for addition are very similar to combining like terms. (2 + 10i) + (-5 + 6i) = -3 + 16i, for example. Subtraction works exactly the same way as addition, except, obviously, we are subtracting real numbers from one another rather than adding them to one another.
Our process of multiplication ought to be familiar as well. Suppose we have (4 + 3i)(6+4i). Using the distributive property, we would end up with 24 + 16i + 18i + 12i^2. Note that when we multiply like terms in which "i" is used, we add the exponents according to our exponent laws. Therefore, i times i equals i^2. Finally, we add like terms, and we get 24 + 34i^2 + 12i^2.