Incercam sa-l scriem pe [tex]z^5[/tex] sub forma trigonometrica:
[tex]z^5=\dfrac{1}{2}+\dfrac{\sqrt{3}}{2}i=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}[/tex]
De aici, se afla usor radacinile, conform formulei:
[tex]z_k=\cos\dfrac{\frac{\pi}{3}+2k\pi}{5}+i\sin\dfrac{\frac{\pi}{3}+2k\pi}{5}[/tex]
unde [tex]k[/tex] ia toate valorile de la 0 la 4 (vom avea deci 5 radacini in total).
