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受欢迎的代数 >

x^2=sqrt(-1)

解答

x^{2} = - 1

解答

x = \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}

求解步骤

x^{2} = - 1

使用虚数运算法则:

- 1 = i

x^{2} = 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 = 2, a = i

∣ a ∣ = 1

ar g (a) = \frac{π}{2}

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

化简

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

化简

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

x = \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}

作图

流行的例子

4 (1 - x^{2}) = 1 - x^{2}

x^{2} - 5 x + 4 x = 0

x^{2} 6 = - x

x^{2} - 2 a x + 2 a = 0

4 x^{2} - 42 x + 48 = 0