6: Complex Numbers
( \newcommand{\kernel}{\mathrm{null}\,}\)
- 6.1: Complex Numbers
- Although very powerful, the real numbers are inadequate to solve equations such as x2+1=0, and this is where complex numbers come in.
- 6.2: Polar Form
- In the previous section, we identified a complex number z=a+bi with a point (a,b) in the coordinate plane. There is another form in which we can express the same number, called the polar form.
- 6.3: Roots of Complex Numbers
- A fundamental identity is the formula of De Moivre with which we begin this section.
- 6.4: The Quadratic Formula
- When working with real numbers, we cannot solve the quadratic formula if b2−4ac<0. However, complex numbers allow us to find square roots of negative numbers, and the quadratic formula remains valid for finding roots of the corresponding quadratic equation.
Thumbnail: Argument φ and modulus r locate a point in the complex plane. (CC BY-SA 3.0; Wolfkeeper via Wikipedia)