Appendix A
Complex Numbers
— Leonhard Euler
The set of complex numbers is the set of all numbers of the form where and are real numbers and . This might not be the most formal way of presenting them, but it will do for our purposes!
The way you operate with complex numbers is pretty straightforward. Let , , , and be some real numbers. We add complex numbers as
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Regarding multiplication, we have
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In particular, when , we can deduce that
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Given any complex number , its real part, which we denote as , is , and its imaginary part, which we denote as , is . Moreover, any such number can be represented in the two-dimensional plane as a vector . The length of the resulting vector is said to be the module of , and it is computed as
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If is a complex number, its conjugate is . In layman’s terms, if you want to get the conjugate of any complex number, all you have to do is flip the sign of its imaginary part. It is easy to check that, given any complex...
