Solve the equation $\displaystyle z^3 + 1 = i$ for the unknown complex quantity $\displaystyle z$. Express your answers in rectangular form to two decimal places.
Solve the equation $\displaystyle z^3 + 1 = i$ for the unknown complex quantity $\displaystyle z$. Express your answers in rectangular form to two decimal places.
That means that $\displaystyle z^3=-1+i=\sqrt{2}\left(\cos\left[\frac{3\pi}{4}\right]+i\sin\left[\frac{3\pi}{4}\right]\right)$
Now find the three cube roots.