The real numbers are deficient in the sense that not all algebraic operations on them produce real numbers. Thus, for sqrt(-1) to make sense, we must lift our sights to the domain of complex numbers. Do complex numbers have this same deficiency? That is, if we are to make sense out of expressions like sqrt(1+i) , must we appeal to yet another new number system? The answer to this question is no. It turns out that any reasonable algebraic operation we perform on complex numbers gives us complex numbers. In this respect, we say that the complex numbers are complete. Later we will learn how to evaluate intriguing algebraic expressions such as (-1)^i . For now we will be content to study integral powers and roots of complex numbers.