Algebrický a goniometrický tvar komplexného čísla

9000038604

Časť: 
B
Vyjadrite v goniometrickom tvare dané komplexné číslo. \[ \frac{\sqrt{3}} {\sqrt{2}} + \mathrm{i}\frac{\sqrt{3}} {\sqrt{2}} \]
\(\sqrt{3}\left (\cos \frac{\pi }{4} + \mathrm{i}\sin \frac{\pi }{4}\right )\)
\(\sqrt{3}\left (\cos \frac{3\pi } {4} + \mathrm{i}\sin \frac{3\pi } {4}\right )\)
\(\sqrt{2}\left (\cos \frac{\pi }{3} + \mathrm{i}\sin \frac{\pi }{3}\right )\)
\(\sqrt{2}\left (\cos \frac{2\pi } {3} + \mathrm{i}\sin \frac{2\pi } {3}\right )\)

9000038605

Časť: 
B
Vyjadrite v goniometrickom tvare dané komplexné číslo. \[ -\frac{\sqrt{5}} {2} + \mathrm{i}\frac{\sqrt{15}} {2} \]
\(\sqrt{5}\left (\cos \frac{2\pi } {3} + \mathrm{i}\sin \frac{2\pi } {3}\right )\)
\(\sqrt{5}\left (\cos \frac{\pi }{3} + \mathrm{i}\sin \frac{\pi }{3}\right )\)
\(\sqrt{5}\left (\cos \frac{2\pi } {5} + \mathrm{i}\sin \frac{2\pi } {5}\right )\)
\(\sqrt{5}\left (\cos \frac{3\pi } {2} + \mathrm{i}\sin \frac{3\pi } {2}\right )\)

9000038606

Časť: 
B
Vyjadrite v algebraickom tvare dané komplexné číslo. \[ \cos \frac{\pi } {4} + \mathrm{i}\sin \frac{\pi } {4} \]
\(\frac{\sqrt{2}} {2} + \mathrm{i}\frac{\sqrt{2}} {2} \)
\(\frac{\sqrt{2}} {2} -\mathrm{i}\frac{\sqrt{2}} {2} \)
\(\frac{\sqrt{3}} {2} + \mathrm{i}\frac{\sqrt{3}} {2} \)
\(\frac{\sqrt{3}} {2} -\mathrm{i}\frac{\sqrt{3}} {2} \)

9000037408

Časť: 
B
Vyjadrite v goniometrickom tvare komplexné číslo \[z=\frac{1} {\cos \frac{2\pi } {3} +\mathrm{i}\sin \frac{2\pi } {3} }. \]
\(\cos \frac{4\pi } {3} + \mathrm{i}\sin \frac{4\pi } {3}\)
\(\cos \left (-\frac{4\pi } {3}\right ) + \mathrm{i}\sin \left (-\frac{4\pi } {3}\right )\)
\(\cos \frac{3} {2\pi } + \mathrm{i}\sin \frac{3} {2\pi }\)
\(\cos \frac{3} {2\pi } -\mathrm{i}\sin \frac{3} {2\pi }\)

9000035704

Časť: 
B
Bod na \( A \) obrázku je obrazom komplexného čísla:
\(z = 2\sqrt{2}\left (\cos \frac{3\pi } {4} + \mathrm{i}\sin \frac{3\pi } {4}\right )\)
\(z = 2\sqrt{2}\left (\cos \frac{\pi }{4} -\mathrm{i}\sin \frac{\pi }{4}\right )\)
\(z = 2\sqrt{2}\left (-\cos \frac{\pi }{4} + \mathrm{i}\sin \frac{\pi }{4}\right )\)
\(z = 2\sqrt{2}\left (\cos \frac{5\pi } {4} + \mathrm{i}\sin \frac{5\pi } {4}\right )\)