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受欢迎的代数 >

x^2=sqrt(-16)

解答

x^{2} = - 16

解答

x = 2 + 2 i, x = - 2 - 2 i

求解步骤

x^{2} = - 16

化简

- 16 : 4 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 = 4 i

∣ a ∣ = 4

ar g (a) = \frac{π}{2}

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

化简

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

化简

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

x = 2 + 2 i, x = - 2 - 2 i

作图

流行的例子

根 x^2+8x+25=0

roo t s x^{2} + 8 x + 25 = 0

8 x^{2} + 9 = 313

3 x^{2} + 18 = 15 x

x^{2} - 2 x - 3 = - 4

(4 x)^{2} = l^{2} + l^{2}