Video:How to Add and Subtract Complex Numbers

Transcript:How to Add and Subtract Complex Numbers

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 how to add and subtract complex numbers.

How to Add Complex Numbers

Remember, we can treat the i in complex numbers as a variable, and the real numbers just as coefficients. Let's add the complex numbers two plus i, to one plus seven i. Remember, you want to gather like terms, so you want to add two to one and you want to add i to seven i. So two plus one is just three, and i plus seven i is just eight i. So these two numbers, when you add them together, equals three plus eight i.

How to Subtract Complex Numbers

Subtracting two complex numbers can be done in a very similar way. Here, we're going to subtract the complex number five plus two i by the number one plus four i. What we want to do is distribute the minus sign onto the second complex number. So we're going to subtract one from five to give us four, and subtract four i from two i to give us minus two i. Now we know that this complex number subtracted by this complex number gives us four minus two i.

How are Complex Numbers Used in Math?

Complex numbers can be used to represent positions on a plane with the x axis representing the real line and the y axis representing the imaginary line. Given a point on the plane, adding or subtracting a complex number to this point just acts as shifting this point to a new point on the plane.

In general, adding and subtracting complex numbers is a part of a larger feature of complex numbers which help scientists model fluids, weigh propagations, and even electrical circuits. And that's how you add and subtract complex numbers.

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