## Complex Numbers

Complex Numbers Introduction If we try to solve x2 = -1, what happens? We extract square roots to get x = +/- (-1. But if we try to evaluate the square root of ?1 on a scientific calculator, we get ERROR! But still, we need a way to define solutions like this so it is defined that i2 = -1 and thus i = ((-1). This means that the solutions of x2 = -1 are x = i and x = -i We refer to such solutions as Complex Solutions. Furthermore, we refer to a number containing the quantity ?i?, where i = (-1, as an imaginary number. This choice of words ?imaginary? is actually not appropriate, since we use the number ?i? in many real-world engineering applications! Using Complex Numbers To Evaluate Square Roots