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人気のある代数 >

y^8=1

解

y^{8} = 1

解

y = 1, y = - 1, y = i, y = - i, y = \frac{1}{2} + \frac{1}{2} i, y = - \frac{1}{2} - \frac{1}{2} i, y = \frac{1}{2} - \frac{1}{2} i, y = - \frac{1}{2} + \frac{1}{2} i

解答ステップ

y^{8} = 1

equationを

u = y^{2}

と以下で書き換える:

u^{4} = y^{8}

u^{4} = 1

解く

u^{4} = 1 : u = 1, u = - 1, u = i, u = - i

u = 1, u = - 1, u = i, u = - i

再び

u = y^{2}

に置き換えて以下を解く:

y

解く

y^{2} = 1 : y = 1, y = - 1

解く

y^{2} = - 1 : y = i, y = - i

解く

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

解く

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

解答は

y = 1, y = - 1, y = i, y = - i, y = \frac{1}{2} + \frac{1}{2} i, y = - \frac{1}{2} - \frac{1}{2} i, y = \frac{1}{2} - \frac{1}{2} i, y = - \frac{1}{2} + \frac{1}{2} i

グラフ

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