Question 1.b - Raíces de números complejos · Álgebra UOC Juny 2023

Question 1 (25% of final grade). Complex numbers

Solve the following items involving complex numbers:

b.

Calculate all fourth roots of the given complex number and write the solutions in polar representation $r_\theta$ with the arguments $\theta \in [0, 2\pi)$:

$$\sqrt[4]{81\left(\cos\frac{2\pi}{3} + i\sin\frac{2\pi}{3}\right)}$$

$\theta_0 =$

$\theta_1 =$

$\theta_2 =$

$\theta_3 =$