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受欢迎的代数 >

z^4=128+128sqrt(3)i

解答

z^{4} = 128 + 1283 i

解答

z = (6 + 2) + i (- 2 + 6), z = (2 - 6) + i (2 + 6), z = (- 6 - 2) + i (2 - 6), z = (6 - 2) + i (- 2 - 6)

求解步骤

z^{4} = 128 + 1283 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 = 4, a = 128 + 1283 i

∣ a ∣ = 256

ar g (a) = \frac{π}{3}

z = 4256 (cos (\frac{\frac{π}{3} + 2 \cdot 0 π}{4}) + i sin (\frac{\frac{π}{3} + 2 \cdot 0 π}{4})), z = 4256 (cos (\frac{\frac{π}{3} + 2 \cdot 1 π}{4}) + i sin (\frac{\frac{π}{3} + 2 \cdot 1 π}{4})), z = 4256 (cos (\frac{\frac{π}{3} + 2 \cdot 2 π}{4}) + i sin (\frac{\frac{π}{3} + 2 \cdot 2 π}{4})), z = 4256 (cos (\frac{\frac{π}{3} + 2 \cdot 3 π}{4}) + i sin (\frac{\frac{π}{3} + 2 \cdot 3 π}{4}))

化简

4256 (cos (\frac{\frac{π}{3} + 2 \cdot 0 π}{4}) + i sin (\frac{\frac{π}{3} + 2 \cdot 0 π}{4})) : (6 + 2) + i (- 2 + 6)

化简

4256 (cos (\frac{\frac{π}{3} + 2 \cdot 1 π}{4}) + i sin (\frac{\frac{π}{3} + 2 \cdot 1 π}{4})) : (2 - 6) + i (2 + 6)

化简

4256 (cos (\frac{\frac{π}{3} + 2 \cdot 2 π}{4}) + i sin (\frac{\frac{π}{3} + 2 \cdot 2 π}{4})) : (- 6 - 2) + i (2 - 6)

化简

4256 (cos (\frac{\frac{π}{3} + 2 \cdot 3 π}{4}) + i sin (\frac{\frac{π}{3} + 2 \cdot 3 π}{4})) : (6 - 2) + i (- 2 - 6)

z = (6 + 2) + i (- 2 + 6), z = (2 - 6) + i (2 + 6), z = (- 6 - 2) + i (2 - 6), z = (6 - 2) + i (- 2 - 6)

流行的例子

2 x^{6} + 7 x^{3} = 15

x + 1 = x^{3} - 2 x - 5

8 x^{4} + 10 x^{2} - 3 = 0

4x^3+12x^2-25x-75=0

4 x^{3} + 12 x^{2} - 25 x - 75 = 0

y^{3} - y = 0