2. Zadatak

$$z^5i+(1-i)\cdot z^2=0$$ $$z^2\left(z^3i+(1-i)\right)=0$$ $$z^2=0\quad\Longleftrightarrow\quad z=0\quad\text{(dvostruko rješenje)}$$ $$z^3i+(1-i)=0$$ $$z^3=\frac{-1+i}{i}=1+i$$ $$z^3=\sqrt2\left(\cos\frac\pi4+i\sin\frac\pi4\right)$$ $$z_k=\sqrt[6]{2}\left(\cos\frac{\frac\pi4+2k\pi}{3}+i\sin\frac{\frac\pi4+2k\pi}{3}\right),\qquad k=0,1,2$$

Rješenja jednadžbe su:

$$z_0=\sqrt[6]{2}\left(\cos\frac\pi{12}+i\sin\frac\pi{12}\right),$$ $$z_1=\sqrt[6]{2}\left(\cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4}\right),$$ $$z_2=\sqrt[6]{2}\left(\cos\frac{17\pi}{12}+i\sin\frac{17\pi}{12}\right)$$

i dvostruko rješenje $z=0$.