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受欢迎的代数 >

x^2-4=sqrt(-7)

解答

x^{2} - 4 = - 7

解答

x = 423 cos \frac{arctan ( \frac{7}{4} )}{2} + 423 i sin \frac{arctan ( \frac{7}{4} )}{2}, x = 423 cos \frac{arctan ( \frac{7}{4} ) + 2 π}{2} + 423 i sin \frac{arctan ( \frac{7}{4} ) + 2 π}{2}

求解步骤

x^{2} - 4 = - 7

展开

- 7 : 7 i

x^{2} - 4 = 7 i

将

4

到右边

x^{2} = 7 i + 4

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 = 7 i + 4

∣ a ∣ = 23

ar g (a) = arctan (\frac{7}{4})

x = 23 cos \frac{arctan ( \frac{7}{4} ) + 2 \cdot 0 π}{2} + i sin \frac{arctan ( \frac{7}{4} ) + 2 \cdot 0 π}{2}, x = 23 cos \frac{arctan ( \frac{7}{4} ) + 2 \cdot 1 π}{2} + i sin \frac{arctan ( \frac{7}{4} ) + 2 \cdot 1 π}{2}

化简

23 cos \frac{arctan ( \frac{7}{4} ) + 2 \cdot 0 π}{2} + i sin \frac{arctan ( \frac{7}{4} ) + 2 \cdot 0 π}{2} : 423 cos \frac{arctan ( \frac{7}{4} )}{2} + 423 i sin \frac{arctan ( \frac{7}{4} )}{2}

化简

23 cos \frac{arctan ( \frac{7}{4} ) + 2 \cdot 1 π}{2} + i sin \frac{arctan ( \frac{7}{4} ) + 2 \cdot 1 π}{2} : 423 cos \frac{arctan ( \frac{7}{4} ) + 2 π}{2} + 423 i sin \frac{arctan ( \frac{7}{4} ) + 2 π}{2}

x = 423 cos \frac{arctan ( \frac{7}{4} )}{2} + 423 i sin \frac{arctan ( \frac{7}{4} )}{2}, x = 423 cos \frac{arctan ( \frac{7}{4} ) + 2 π}{2} + 423 i sin \frac{arctan ( \frac{7}{4} ) + 2 π}{2}

作图

流行的例子

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