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人気のある代数 >

z^4=-2-2sqrt(3)

解

z^{4} = - 2 - 23

解

z = 4 \frac{1 + 3}{2} + \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i, z = - 4 \frac{1 + 3}{2} - \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i, z = 4 \frac{1 + 3}{2} - \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i, z = - 4 \frac{1 + 3}{2} + \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i

解答ステップ

z^{4} = - 2 - 23

equationを

u = z^{2}

と以下で書き換える:

u^{2} = z^{4}

u^{2} = - 2 - 23

解く

u^{2} = - 2 - 23 : u = 2 + 23 i, u = - 2 + 23 i

u = 2 + 23 i, u = - 2 + 23 i

再び

u = z^{2}

に置き換えて以下を解く:

z

解く

z^{2} = 2 + 23 i : z = 4 \frac{1 + 3}{2} + \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i, z = - 4 \frac{1 + 3}{2} - \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i

解く

z^{2} = - 2 + 23 i : z = 4 \frac{1 + 3}{2} - \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i, z = - 4 \frac{1 + 3}{2} + \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i

解答は

z = 4 \frac{1 + 3}{2} + \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i, z = - 4 \frac{1 + 3}{2} - \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i, z = 4 \frac{1 + 3}{2} - \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i, z = - 4 \frac{1 + 3}{2} + \frac{2 + 2 3}{2 ^{\frac{3}{4}} 4 1 + 3} i

グラフ

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