Complex

Complex numbers

\[ i = \sqrt{-1} \]

\[ a + bi = c + di \iff c = a, d = b \]

\[ (a + bi)(c + di) = ac + adi + bci + bdii = ac + adi + bci - bd = (ac - bd) + (ad + bc)i \]

\[ (a + bi)^2 = (aa - bb) + (ab + ab)i = (a^2 - b^2) + 2abi \]

f is the definition of \(sin(\theta)\)

g is the definition of \(cos(\theta)\)

\(\theta\) is the angle from the right of the x axis to the line h