ko

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

인기 있는 대수학 >

x^6=36sqrt(3)+36i

해법

x^{6} = 363 + 36 i

해법

x = 672 cos (\frac{π}{36}) + 672 i sin (\frac{π}{36}), x = 672 cos (\frac{13 π}{36}) + 672 i sin (\frac{13 π}{36}), x = 672 cos (\frac{25 π}{36}) + 672 i sin (\frac{25 π}{36}), x = 672 cos (\frac{37 π}{36}) + 672 i sin (\frac{37 π}{36}), x = 672 cos (\frac{49 π}{36}) + 672 i sin (\frac{49 π}{36}), x = 672 cos (\frac{61 π}{36}) + 672 i sin (\frac{61 π}{36})

솔루션 단계

x^{6} = 363 + 36 i

위한

z^{n} = a

해결책은

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

n = 6, a = 363 + 36 i

위한

∣ a ∣ = 72

ar g (a) = \frac{π}{6}

x = 672 (cos (\frac{\frac{π}{6} + 2 \cdot 0 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 0 π}{6})), x = 672 (cos (\frac{\frac{π}{6} + 2 \cdot 1 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 1 π}{6})), x = 672 (cos (\frac{\frac{π}{6} + 2 \cdot 2 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 2 π}{6})), x = 672 (cos (\frac{\frac{π}{6} + 2 \cdot 3 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 3 π}{6})), x = 672 (cos (\frac{\frac{π}{6} + 2 \cdot 4 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 4 π}{6})), x = 672 (cos (\frac{\frac{π}{6} + 2 \cdot 5 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 5 π}{6}))

672 (cos (\frac{\frac{π}{6} + 2 \cdot 0 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 0 π}{6}))

단순화하세요:

672 cos (\frac{π}{36}) + 672 i sin (\frac{π}{36})

672 (cos (\frac{\frac{π}{6} + 2 \cdot 1 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 1 π}{6}))

단순화하세요:

672 cos (\frac{13 π}{36}) + 672 i sin (\frac{13 π}{36})

672 (cos (\frac{\frac{π}{6} + 2 \cdot 2 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 2 π}{6}))

단순화하세요:

672 cos (\frac{25 π}{36}) + 672 i sin (\frac{25 π}{36})

672 (cos (\frac{\frac{π}{6} + 2 \cdot 3 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 3 π}{6}))

단순화하세요:

672 cos (\frac{37 π}{36}) + 672 i sin (\frac{37 π}{36})

672 (cos (\frac{\frac{π}{6} + 2 \cdot 4 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 4 π}{6}))

단순화하세요:

672 cos (\frac{49 π}{36}) + 672 i sin (\frac{49 π}{36})

672 (cos (\frac{\frac{π}{6} + 2 \cdot 5 π}{6}) + i sin (\frac{\frac{π}{6} + 2 \cdot 5 π}{6}))

단순화하세요:

672 cos (\frac{61 π}{36}) + 672 i sin (\frac{61 π}{36})

x = 672 cos (\frac{π}{36}) + 672 i sin (\frac{π}{36}), x = 672 cos (\frac{13 π}{36}) + 672 i sin (\frac{13 π}{36}), x = 672 cos (\frac{25 π}{36}) + 672 i sin (\frac{25 π}{36}), x = 672 cos (\frac{37 π}{36}) + 672 i sin (\frac{37 π}{36}), x = 672 cos (\frac{49 π}{36}) + 672 i sin (\frac{49 π}{36}), x = 672 cos (\frac{61 π}{36}) + 672 i sin (\frac{61 π}{36})

인기 있는 예

x (x - 3)^{2} = 2 x

(x-3)^7=64(x-3)^4

(x - 3)^{7} = 64 (x - 3)^{4}

- 16 y - y^{3} + 32 = 0

x^{3} - 3 = - 30

(x-1)(x-2)(x+1)=0

(x - 1) (x - 2) (x + 1) = 0