Lec 6 | MIT 18.03 Differential Equations, Spring 2006
Complex Numbers and Complex Exponentials. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information ...
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I assume from high school you know how to add and multiply complex numbers using the relation i squared equals negative one. I'm a little less certain that you remember how to divide them. I hope you read last night by way of preparation for that, but since that's something we're going to have to do a lot of a differential equations, so remember that the division is done by making use of the complex conjugate. So, if z is equal to a plus bi, some people write a plus ib, and sometimes I'll do that too if it's more convenient. Then, the complex conjugate is what you get by changing i to negative i. And, the important thing is that the product of those two is a real number. The product of these is a squared minus the quantity ib all squared, which makes a squared plus b squ...
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I assume from high school you know how to add and multiply complex numbers using the relation i squared equals negative one. I'm a little less certain that you remember how to divide them. I hope you read last night by way of preparation for that, but since that's something we're going to have to do a lot of a differential equations, so remember that the division is done by making use of the complex conjugate. So, if z is equal to a plus bi, some people write a plus ib, and sometimes I'll do that too if it's more convenient. Then, the complex conjugate is what you get by changing i to negative i. And, the important thing is that the product of those two is a real number. The product of these is a squared minus the quantity ib all squared, which makes a squared plus b squ...
