Exponential Form (Edexcel A-Level Further Mathematics): Flashcards

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

$z = re^{i\theta}$

$z_1z_2 = r_1r_2e^{i(\theta_1+\theta_2)}$

$\frac{r_1}{r_2}e^{i(\theta_1-\theta_2)}$

$\frac{1}{2}(e^{i\theta} + e^{-i\theta})$

$\frac{1}{2i}(e^{i\theta} - e^{-i\theta})$

$\arg(z_1) + \arg(z_2)$

$|z_1| \times |z_2|$

$-1$

$\cos\theta - i\sin\theta$