Complex Numbers

A complex number is a number of the form Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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, ${\sqrt {-25}}=5{\sqrt {-1}}=5i$). $i^{2}=-1$, $i^{3}=-i$, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i^4 = 1 } , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i^5 = i } again, and so on.

Resources

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