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人気のある代数 >

z^6-(3+2i)z^3+2+2i=0

解

z^{6} - (3 + 2 i) z^{3} + 2 + 2 i = 0

解

z = 1, z = - \frac{1}{2} + \frac{3}{2} i, z = - \frac{1}{2} - \frac{3}{2} i, z = \frac{1 + 3}{2} + i \frac{- 1 + 3}{2}, z = - 1 + i, z = \frac{1 - 3}{2} + i \frac{- 1 - 3}{2}

解答ステップ

z^{6} - (3 + 2 i) z^{3} + 2 + 2 i = 0

改良

(z^{6} - 3 z^{3} + 2) + i (2 - 2 z^{3}) = 0

標準的な形式で書く

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

z^{6} - (3 + 2 i) z^{3} + 2 + 2 i = 0

equationを

u = z^{3}

と以下で書き換える:

u^{2} = z^{6}

u^{2} - (3 + 2 i) u + 2 + 2 i = 0

解く

u^{2} - (3 + 2 i) u + 2 + 2 i = 0 : u = 1, u = 2 + 2 i

u = 1, u = 2 + 2 i

再び

u = z^{3}

に置き換えて以下を解く:

z

解く

z^{3} = 1 : z = 1, z = - \frac{1}{2} + \frac{3}{2} i, z = - \frac{1}{2} - \frac{3}{2} i

解く

z^{3} = 2 + 2 i : z = \frac{1 + 3}{2} + i \frac{- 1 + 3}{2}, z = - 1 + i, z = \frac{1 - 3}{2} + i \frac{- 1 - 3}{2}

解答は

z = 1, z = - \frac{1}{2} + \frac{3}{2} i, z = - \frac{1}{2} - \frac{3}{2} i, z = \frac{1 + 3}{2} + i \frac{- 1 + 3}{2}, z = - 1 + i, z = \frac{1 - 3}{2} + i \frac{- 1 - 3}{2}

人気の例

根 x^3-3x^2-10x+24

roo t s x^{3} - 3 x^{2} - 10 x + 24

x^3-x^2-25x+25=0

x^{3} - x^{2} - 25 x + 25 = 0

3y^3-20y^2-7y=0

3 y^{3} - 20 y^{2} - 7 y = 0

4 x^{3} - 5 x + 2 = 24

2x^3-6x^2+13x-14=0

2 x^{3} - 6 x^{2} + 13 x - 14 = 0