9000035810 | math4u.vsb.cz

Podoblasť:

Mocniny a odmocniny komplexných čísel

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Project ID:

9000035810

Accepted:

1

Clonable:

0

Easy:

0

Je dané komplexné číslo

z = - 2 + 2 i

. Všetky navzájom rôzne hodnoty

\sqrt[3]{z}

sú:

\begin{aligned} w_{0} = \sqrt[6]{8} (\cos \frac{π}{4} + i \sin \frac{π}{4}) \\ w_{1} = \sqrt[6]{8} (\cos \frac{11 π}{12} + i \sin \frac{11 π}{12}) \\ w_{2} = \sqrt[6]{8} (\cos \frac{19 π}{12} + i \sin \frac{19 π}{12}) \end{aligned}

\begin{aligned} w_{0} = 2 (\cos \frac{π}{4} + i \sin \frac{π}{4}) \\ w_{1} = 2 (\cos \frac{11 π}{12} + i \sin \frac{11 π}{12}) \\ w_{2} = 2 (\cos \frac{19 π}{12} + i \sin \frac{19 π}{12}) \end{aligned}

\sqrt[3]{- 2} + \sqrt[3]{2}

\begin{aligned} w_{0} = 2 (\cos \frac{π}{3} + i \sin \frac{π}{3}) \\ w_{1} = 2 (\cos π + i \sin π) \\ w_{2} = 2 (\cos \frac{5 π}{3} + i \sin \frac{5 π}{3}) \end{aligned}