What Is a Complex Number?
Question
A complex number is made up of a real part and
00:00
00:00
Hi, my name is Bassem Saad. I'm a Math Ph.D. candidate at U.C. Davis, and I'm here today for About.com to show you what a complex number is.A complex number is made up of a real part and imaginary part. For example, five minus three i is a complex number. Remember, i can be treated like a variable with the added property that i squared equals negative one. We can treat complex numbers like a little polynomial, and just like polynomials, we can add, subtract, multiply, and divide complex numbers with just a few extra tricks.Say five minus three i, and another complex number, plus two plus i. Well, just like a polynomial you want to collect like-terms. So five and two are real numbers, so we just collect them – five plus two. And i's are our variables, so we collect their coefficients-- that is plus minus three (and there's a one right there), plus one i. So the complex number five minus three i plus two plus i equals seven minus two i.  Complex numbers are vastly important to mathematics with applications from algebra to calculus. Thanks for watching, and to learn more, visit us on the web at About.com.