Trois conversions expliquées

Application

On donne la forme trigonométrique de plusieurs nombres complexes :

$z_1 = 2 = 2(1+0i) = 2(\cos0+i\sin0) = [2,0]$

$z_2 = -5 = 5(-1+0i) = 5(\cos\pi+i\sin\pi) = [5,\pi]$

$z_3 = 7i = 7(0+i) = 7\left(\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}\right) = \left[7,\frac{\pi}{2}\right]$

$z_4 = -\frac{3}{5}i = \frac{3}{5}(0-i) = \frac{3}{5}\left(\cos\left(-\frac{\pi}{2}\right)+i\sin\left(-\frac{\pi}{2}\right)\right) = \left[\frac{3}{5},-\frac{\pi}{2}\right]$

$z_5 = 1+i = \sqrt2\left(\frac{\sqrt2}{2}+\frac{\sqrt2}{2}i\right) = \sqrt2\left(\cos\frac{\pi}{4}+i\sin\frac{\pi}{4}\right) = \left[\sqrt2,\frac{\pi}{4}\right]$