Seja z um número complexo e i a unidade imaginária. Determine z de forma que o triângul...

z = $\frac{\left(\sqrt{3}-\sqrt{2}\right)e^{{}^{\frac{-5\pi i}{4}}}}{2}$ ou z = $-\frac{\left(\sqrt{3}+\sqrt{2}\right)e^{{}^{\frac{\pi i}{4}}}}{2}$

z = $\frac{\left(\sqrt{5}+\sqrt{3}\right)e^{{}^{\frac{\pi i}{6}}}}{2}$ ou z = $\frac{\left(\sqrt{5}-\sqrt{3}\right)e^{{}^{\frac{-\pi i}{6}}}}{2}$

z = $\frac{\left(\sqrt{6}+\sqrt{3}\right)e^{{}^{\frac{-3\pi i}{4}}}}{2}$ ou z = $\frac{\left(\sqrt{6}-\sqrt{3}\right)e^{{}^{\frac{\pi i}{4}}}}{2}$

z = $\frac{\left(\sqrt{6}-\sqrt{2}\right)e^{{}^{\frac{\pi i}{4}}}}{2}$ ou z = $\frac{\left(\sqrt{6}+\sqrt{2}\right)e^{{}^{\frac{5\pi i}{4}}}}{2}$

z = $\frac{\left(\sqrt{3}+\sqrt{2}\right)e^{{}^{\frac{11\pi i}{6}}}}{2}$ ou z = $\frac{\left(\sqrt{3}-\sqrt{2}\right)e^{{}^{\frac{\pi i}{6}}}}{2}$