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受欢迎的代数 >

x^6=32sqrt(3)+32i

解答

x^{6} = 323 + 32 i

解答

x = 2 cos (\frac{π}{36}) + 2 i sin (\frac{π}{36}), x = 2 cos (\frac{13 π}{36}) + 2 i sin (\frac{13 π}{36}), x = 2 cos (\frac{25 π}{36}) + 2 i sin (\frac{25 π}{36}), x = 2 cos (\frac{37 π}{36}) + 2 i sin (\frac{37 π}{36}), x = 2 cos (\frac{49 π}{36}) + 2 i sin (\frac{49 π}{36}), x = 2 cos (\frac{61 π}{36}) + 2 i sin (\frac{61 π}{36})

求解步骤

x^{6} = 323 + 32 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 = 6, a = 323 + 32 i

∣ a ∣ = 64

ar g (a) = \frac{π}{6}

x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 0 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 0 π}{6})), x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 1 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 1 π}{6})), x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 2 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 2 π}{6})), x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 3 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 3 π}{6})), x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 4 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 4 π}{6})), x = 664 (cos (\frac{\frac{π}{6} + 2 \cdot 5 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 5 π}{6}))

化简

664 (cos (\frac{\frac{π}{6} + 2 \cdot 0 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 0 π}{6})) : 2 cos (\frac{π}{36}) + 2 i sin (\frac{π}{36})

化简

664 (cos (\frac{\frac{π}{6} + 2 \cdot 1 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 1 π}{6})) : 2 cos (\frac{13 π}{36}) + 2 i sin (\frac{13 π}{36})

化简

664 (cos (\frac{\frac{π}{6} + 2 \cdot 2 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 2 π}{6})) : 2 cos (\frac{25 π}{36}) + 2 i sin (\frac{25 π}{36})

化简

664 (cos (\frac{\frac{π}{6} + 2 \cdot 3 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 3 π}{6})) : 2 cos (\frac{37 π}{36}) + 2 i sin (\frac{37 π}{36})

化简

664 (cos (\frac{\frac{π}{6} + 2 \cdot 4 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 4 π}{6})) : 2 cos (\frac{49 π}{36}) + 2 i sin (\frac{49 π}{36})

化简

664 (cos (\frac{\frac{π}{6} + 2 \cdot 5 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 5 π}{6})) : 2 cos (\frac{61 π}{36}) + 2 i sin (\frac{61 π}{36})

x = 2 cos (\frac{π}{36}) + 2 i sin (\frac{π}{36}), x = 2 cos (\frac{13 π}{36}) + 2 i sin (\frac{13 π}{36}), x = 2 cos (\frac{25 π}{36}) + 2 i sin (\frac{25 π}{36}), x = 2 cos (\frac{37 π}{36}) + 2 i sin (\frac{37 π}{36}), x = 2 cos (\frac{49 π}{36}) + 2 i sin (\frac{49 π}{36}), x = 2 cos (\frac{61 π}{36}) + 2 i sin (\frac{61 π}{36})

流行的例子

x^{6} = 729

0 = x^{3} - 12 x

4*5-3=1+x^5+x-8

4 \cdot 5 - 3 = 1 + x^{5} + x - 8

x^{4} - 2 x - 1 = 0

x^4-16x^2+225=0

x^{4} - 16 x^{2} + 225 = 0