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受欢迎的代数 >

w^3=-2-2sqrt(3)i

解答

w^{3} = - 2 - 23 i

解答

w = 34 cos (\frac{2 π}{9}) - 34 i sin (\frac{2 π}{9}), w = 34 cos (\frac{4 π}{9}) + 34 i sin (\frac{4 π}{9}), w = 34 cos (\frac{10 π}{9}) + 34 i sin (\frac{10 π}{9})

求解步骤

w^{3} = - 2 - 23 i

For

z^{n} = a

the solutions are

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

对于

n = 3, a = - 2 - 23 i

∣ a ∣ = 4

ar g (a) = \frac{π}{3} - π

w = 34 (cos (\frac{\frac{π}{3} - π + 2 \cdot 0 π}{3}) + i sin (\frac{\frac{π}{3} - π + 2 \cdot 0 π}{3})), w = 34 (cos (\frac{\frac{π}{3} - π + 2 \cdot 1 π}{3}) + i sin (\frac{\frac{π}{3} - π + 2 \cdot 1 π}{3})), w = 34 (cos (\frac{\frac{π}{3} - π + 2 \cdot 2 π}{3}) + i sin (\frac{\frac{π}{3} - π + 2 \cdot 2 π}{3}))

化简

34 (cos (\frac{\frac{π}{3} - π + 2 \cdot 0 π}{3}) + i sin (\frac{\frac{π}{3} - π + 2 \cdot 0 π}{3})) : 34 cos (\frac{2 π}{9}) - 34 i sin (\frac{2 π}{9})

化简

34 (cos (\frac{\frac{π}{3} - π + 2 \cdot 1 π}{3}) + i sin (\frac{\frac{π}{3} - π + 2 \cdot 1 π}{3})) : 34 cos (\frac{4 π}{9}) + 34 i sin (\frac{4 π}{9})

化简

34 (cos (\frac{\frac{π}{3} - π + 2 \cdot 2 π}{3}) + i sin (\frac{\frac{π}{3} - π + 2 \cdot 2 π}{3})) : 34 cos (\frac{10 π}{9}) + 34 i sin (\frac{10 π}{9})

w = 34 cos (\frac{2 π}{9}) - 34 i sin (\frac{2 π}{9}), w = 34 cos (\frac{4 π}{9}) + 34 i sin (\frac{4 π}{9}), w = 34 cos (\frac{10 π}{9}) + 34 i sin (\frac{10 π}{9})

流行的例子

solvefor r,v= 4/3 pir^3

so l v e f or r, v = \frac{4}{3} π r^{3}

2 x - 13 = - x^{4} + 6

x^{3} - 2 x^{2} - 3 x = 0

3 x^{4} - 48 x^{2} = 0

6 x^{4} - 54 x^{2} = 0