
# 6: Complex Numbers


• 6.1: Complex Numbers
Although very powerful, the real numbers are inadequate to solve equations such as $$x^2+1=0$$, 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 $$\left( a, b\right)$$ 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.
When working with real numbers, we cannot solve the quadratic formula if $$b^{2}-4ac<0.$$ 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.
• 6.E: Exercises

Thumbnail: Argument $$φ$$ and modulus $$r$$ locate a point in the complex plane. (CC BY-SA 3.0; Wolfkeeper via Wikipedia)