Complexos
Aula 3 e exercícios - Operações na forma trigonométrica
Aula com exemplos
Exercícios resolvidos
3.1) 
Considere os complexos complexos $\displaystyle {z_1} = 2e^{i\frac{\pi }{2}}$, $\displaystyle {z_2} = - 3e^{i\frac{{2\pi }}{3}}$ e $\displaystyle {z_3} = e^{ -i\frac{\pi }{3}}$. Calcule na forma trigonométrica:
| (a) $z_1^{-1}$; | (b) ${z_1} \times {z_2}$; | (c) $\displaystyle\frac{{{z_1}}}{{{z_2}}}$; |
| (d) ${\left( {{z_2}} \right)^9}$; | (e) $\displaystyle\frac{{{z_1}}}{{{{\bar z}_2}}} \times {\bar z_3}$. |
3.2)
Calcule e represente no plano de Argand:
(a) as raízes quadradas de $1 - \sqrt 3 i$;
(b) as
raízes quartas de $\displaystyle - \frac{{\sqrt 2 }}{2} - \frac{{\sqrt 2 }}{2}i$;
(c) as
raízes quintas de $-3i$.