Complex Numbers

A complex number is a number of the form $a+bi$ where $a$ is the real part of the complex number, and $bi$ is the imaginary part of the complex number. If $b=0$, then $a+bi$ is a real number. If $a=0$ and b is not equal to 0, the complex number is called an imaginary number. The imaginary unit $i={\sqrt {-1}}$, and can be used to express other imaginary numbers (for example, ${\sqrt {-25}}=5{\sqrt {-1}}=5i$). $i^{2}=-1$, $i^{3}=-i$, $i^{4}=1$, $i^{5}=i$ again, and so on.

Resources

• Complex Numbers, Paul's Online Notes
• Intro to Complex Numbers, Lumen Learning