Formulari de nombres complexos

$z = a + bi$

$|z| = \sqrt{a^2+b^2}$

$\arg z = \arctan\dfrac{b}{a} \ \text{(mira el quadrant!)}$

$z = r_\alpha$

$z = re^{i\alpha}$

$\bar{z} = a - bi$

$r_\alpha \cdot s_\beta = (rs)_{\alpha+\beta}$

$\dfrac{r_\alpha}{s_\beta} = \left(\dfrac{r}{s}\right)_{\alpha-\beta}$

$(r_\alpha)^n = (r^n)_{n\alpha}$

$i, -1, -i, 1 \ \text{(cicle de 4)}$

$\sqrt[n]{r_\alpha} = \left(\sqrt[n]{r}\right)_{\frac{\alpha + 360°k}{n}}$

$n$ arrels, repartides en un polígon regular

$e^{i\theta} = \cos\theta + i\sin\theta$

$|e^z| = e^{\mathrm{Re}(z)}$