共50条信息
设\(z\)是虚数,\(ω=z+\dfrac{1}{z}\)是实数,且\(-1 < ω < 2\)
\((1)\)求\(|z|\)的值及\(z\)的实部的取值范围;
\((2)\)设\(u=\dfrac{1-z}{1+z} \),求证:\(u\)为纯虚数;
\((3)\)求\(ω-u^{2}\)的最小值
已知\(1+x+x^{2}=0\),求:
\((1)1+x+x^{2}+…+x^{100}\);
\((2)x^{2001}+x^{2002}+…+x^{2007}\).
设\(z\)是复数,\(α(z)\)表示满足\(z^{n}=1\)的最小正整数\(n\),则对虚数单位\(i\),\(α(i)=\) \((\) \()\)
复数\(z{=|}(\sqrt{3}{-}i)i{|+}i^{2017}(i\)为虚数单位\()\),则复数\(z\)的共轭复数为\(({ })\)
复数\( \dfrac{2}{1+i} \)的虚部是\((\) \()\)
已知\(i\)是虚数单位,则\(\left(\begin{matrix} \begin{matrix} \dfrac{ \sqrt{2}}{1-i} \end{matrix}\end{matrix}\right)^2016 +\left(\begin{matrix} \begin{matrix} \dfrac{1+i}{1-i} \end{matrix}\end{matrix}\right)^6 =\)________.
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