Algebrický a goniometrický tvar komplexného čísla

9000035805

Časť: 
B
Sú dané komplexné čísla \[ \text{$a = 2\left (\cos \frac{2\pi } {3} + \mathrm{i}\sin \frac{2\pi } {3}\right )$, $b = \sqrt{2}\left (\cos \frac{3\pi } {4} + \mathrm{i}\sin \frac{3\pi } {4}\right )$.} \] Súčin \(ab\) sa rovná:
\(2\sqrt{2}\left (\cos \frac{17\pi } {12} + \mathrm{i}\sin \frac{17\pi } {12}\right )\)
\(2\sqrt{2}\left (\cos \frac{\pi }{2} + \mathrm{i}\sin \frac{\pi }{2}\right )\)
\(2\sqrt{2}\left (\cos \frac{5\pi } {7} + \mathrm{i}\sin \frac{5\pi } {7}\right )\)
\(2\sqrt{2}\left (\cos \frac{5\pi } {12} + \mathrm{i}\sin \frac{5\pi } {12}\right )\)

9000035806

Časť: 
B
Sú dané komplexné čísla \[ \text{ $a = 2\left (\cos \frac{5\pi } {3} + \mathrm{i}\sin \frac{5\pi } {3}\right )$, $b = 3\left (\cos \frac{11\pi } {6} + \mathrm{i}\sin \frac{11\pi } {6} \right )$.} \] Podiel \(\frac{a} {b}\) sa rovná:
\(\frac{2} {3}\left (\cos \frac{11\pi } {6} + \mathrm{i}\sin \frac{11\pi } {6} \right )\)
\(\frac{2} {3}\left (\cos \frac{\pi } {6} + \mathrm{i}\sin \frac{\pi } {6}\right )\)
\(\frac{2} {3}\left (\cos \frac{5\pi } {6} + \mathrm{i}\sin \frac{5\pi } {6}\right )\)
\(\frac{2} {3}\left (\cos \frac{7\pi } {6} + \mathrm{i}\sin \frac{7\pi } {6}\right )\)

9000035807

Časť: 
A
Sú dané komplexné čísla \(a = 2 - 3\mathrm{i}\), \(b = 1 + 2\mathrm{i}\). Podiel \(\frac{a} {b}\) sa rovná:
\(-\frac{4} {5} -\frac{7} {5}\mathrm{i}\)
\(2 -\frac{3} {2}\mathrm{i}\)
\(\frac{8} {5} -\frac{7} {5}\mathrm{i}\)
\(\frac{4} {3} + \frac{7} {3}\mathrm{i}\)