Chapter: Simple Formulas Involving the Complex Numbers

In this chapter, we derive some useful formulas involving complex numbers which go beyond simple arithmetic operations. In particular, we will derive some properties of the complex absolute value and the real and imaginary parts. Moreover, we will show that, although the complex numbers are an extension of the real numbers, they cannot be ordered like it was the case for the order relation of real numbers.

  1. Proposition: Extracting the Real and the Imaginary Part of a Complex Number
  2. Proposition: Calculating with Complex Conjugates
  3. Proposition: Complex Numbers Cannot Be Ordered
  4. Proposition: Absolute Value of Complex Conjugate
  5. Proposition: Absolute Value of the Product of Complex Numbers

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