Categoria: formulae.app / Matemáticas / Álgebra Lineal / Números Complejos
$$z=a+bi,$$
$$r=|z|=\sqrt{a^2+b^2},\:tan\:\alpha\:=\frac{b}{a}\rightarrow\alpha =tan^{-1}\left(\frac{b}{a}\right)$$
a = r cos α , b= r sen α
Forma trigonométrica
2 = r cos α + (r sin α)i = r(cos α + i sin α)
$$r_a \cdot r'_a = (r \cdot r')_{a+a'}$$
$$\frac{r_a}{r'_a}=\left(\frac{r}{r'}\right)_{a-a'}$$
$$(r_a)^n=r_a \cdot r_a \cdot r_a \cdots r_a = (r^n)_{na}$$
$$z^n=r^n(cos\:n\alpha + i\: sen\:n\alpha)$$
$$\sqrt[n]{r_{\alpha}}=(\sqrt[n]{r})_{\frac{\alpha+360_ok}{n}}$$
$$i^0=1,\qquad i^1=i, \qquad i^2=-1$$
$$i^0=-i,\qquad i^4=1, \qquad i^5=i$$
$$\cdots$$