Complex numbers — Basic example

- [Tutor] What is the sum of the complex numbers 1 + 2i and 5 - 7i, where i is equal to the square root of - 1. Pause this video and see if you can figure. All right, now let's do this together. And the main realization when you are adding or subtracting complex numbers, is to recognize that you can get your sum or difference by adding or subtracting the real parts and then separately adding or subtracting the complex parts. So, one way to think about it. Let me just rewrite these numbers 1 + 2i and then + 5 - 7i. We could rewrite this as 1 + 5. So, let me write that 1 + 5 that's the real part, plus we see 2i - 7i, + 2i - 7i, and so what's that going to get us? Well, we have six and then we have + 2i - 7i that is - 5i. So, plus - 5i is the same thing we can just subtract 5i right over here. So, 6 - 5i, which is choice C.