A

9000037507

Část: 
A
Určete podíl \(\frac{a} {b}\) komplexních čísel \(a\), \(b\). \[ a = \sqrt{3} + 2\mathrm{i},\quad b = \sqrt{2} -\mathrm{i} \]
\(\frac{\sqrt{6}-2} {3} + \mathrm{i}\frac{2\sqrt{2}+\sqrt{3}} {3} \)
\(\frac{\sqrt{6}-2} {3} -\mathrm{i}\frac{2\sqrt{2}+\sqrt{3}} {3} \)
\(\frac{\sqrt{6}-3} {2} + \mathrm{i}\frac{2\sqrt{2}+\sqrt{3}} {2} \)
\(\frac{\sqrt{6}-2} {2} -\mathrm{i}\frac{2\sqrt{2}+\sqrt{3}} {2} \)

9000037403

Část: 
A
Určete \(z^{4}\), když \(z = \sqrt{3}\left (\cos \frac{\pi }{3} + \mathrm{i}\sin \frac{\pi }{3}\right )\).
\(-\frac{9} {2} -\frac{9\mathrm{i}\sqrt{3}} {2} \)
\(\frac{9} {2} + \frac{9\mathrm{i}\sqrt{3}} {2} \)
\(\frac{3} {2}\)
\(-\frac{3} {2}\)