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人気のある代数 >

x^2-4=sqrt(-7)

解

x^{2} - 4 = - 7

解

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}

解答ステップ

x^{2} - 4 = - 7

拡張

- 7 : 7 i

x^{2} - 4 = 7 i

4

を右側に移動します

x^{2} = 7 i + 4

z^{n} = a

の場合, 解は

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

以下のため:

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}

簡素化

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}

簡素化

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}

グラフ

人気の例

completesquare z^2+4z

co m pl e t es q u a re z^{2} + 4 z

x^2+((4-x)/2)^2=16

x^{2} + (\frac{4 - x}{2})^{2} = 16

completesquare 3x^2-6x-10

co m pl e t es q u a re 3 x^{2} - 6 x - 10

m^{2} = 5 m + 14

x^{2} + 2 x + 10 = - 2