Question

Sa se rezolve in C ecuatia

Answer 1

Incercam sa-l scriem pe $z^5$ sub forma trigonometrica:

$z^5=\dfrac{1}{2}+\dfrac{\sqrt{3}}{2}i=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}$

De aici, se afla usor radacinile, conform formulei:

$z_k=\cos\dfrac{\frac{\pi}{3}+2k\pi}{5}+i\sin\dfrac{\frac{\pi}{3}+2k\pi}{5}$

unde $k$ ia toate valorile de la 0 la 4 (vom avea deci 5 radacini in total).