Simply Math

Arithmetic Operations

Example: \( ab + ac = a (b+c) \)

Example: \( a( \frac{a}{c} ) = \frac{ab}{c} \)

Example: \( \frac{ \frac{a}{b} }{c} = \frac{a}{bc} \)

Example: \( \frac{ab + ac}{a} = b+c, a \neq 0 \)

Example: \( \frac{ \frac{a}{b}}{ \frac{c}{d}} = \frac{ad}{bc} \)

Properties of Radicals

Example: \( \sqrt[n]{a} = a ^ \frac{1}{n} \)

Example: \( \sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b} \)

Example: \( \sqrt[m]{ \sqrt[n]{a}} = \sqrt[nm]{a} \)

Example: \( \sqrt[n]{ \frac{a}{b}} = \frac{ \sqrt[n]{a} }{ \sqrt[n]{b} } \)

Complex Numbers

Example: \( \left| a+bi \right| = \sqrt{a^2+b^2} \)

Complex Conjugate

\( \stackrel{\rule{3em}{1pt}}{(a+bi)} (a+bi) = \left| a+bi \right| ^2 \)

Hyperbola

\( \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1 \)