de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

w^3=i

Lösung

w^{3} = i

Lösung

w = \frac{3}{2} + i \frac{1}{2}, w = - \frac{3}{2} + i \frac{1}{2}, w = - i

Schritte zur Lösung

w^{3} = i

Für

z^{n} = a

sind die Lösungen

z_{k} = n ∣ a ∣ (cos (\frac{ar g ( a ) + 2 kπ}{n}) + i sin (\frac{ar g ( a ) + 2 kπ}{n})),

k = 0, 1, \dots, n - 1

Für

n = 3, a = i

∣ a ∣ = 1

ar g (a) = \frac{π}{2}

w = 31 (cos (\frac{\frac{π}{2} + 2 \cdot 0 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 0 π}{3})), w = 31 (cos (\frac{\frac{π}{2} + 2 \cdot 1 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 1 π}{3})), w = 31 (cos (\frac{\frac{π}{2} + 2 \cdot 2 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 2 π}{3}))

Vereinfache

31 (cos (\frac{\frac{π}{2} + 2 \cdot 0 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 0 π}{3})) : \frac{3}{2} + i \frac{1}{2}

Vereinfache

31 (cos (\frac{\frac{π}{2} + 2 \cdot 1 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 1 π}{3})) : - \frac{3}{2} + i \frac{1}{2}

Vereinfache

31 (cos (\frac{\frac{π}{2} + 2 \cdot 2 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 2 π}{3})) : - i

w = \frac{3}{2} + i \frac{1}{2}, w = - \frac{3}{2} + i \frac{1}{2}, w = - i

Beliebte Beispiele

z^{3} = \frac{i}{8}

x^{2} (x - 6) = 0

z^{4} = 1 + i

5 x^{3} - 6 x^{2} - 7 = 0

0 = x^{4} - 2 x^{2} - 8