设\(z=(i-1)i^{3}(i\)是虚数单位\()\)，则\(\overline{z}=\)

\((1)\)计算\({{\log }_{2.5}}6.25+\lg \dfrac{1}{100}+\ln \sqrt{e}+{{2}^{1+{{\log }_{2}}3}} =\)______．

\((2){{\left( \sqrt{x}-\dfrac{i}{x} \right)}^{8}}\)的二项展开式中，含\(x\)的一次项的系数为         \(.(\)用数字作答\()\)

\((3)\)两圆\({{x}^{2}}+{{y}^{2}}+2ax+{{a}^{2}}-4=0\)和\({{x}^{2}}+{{y}^{2}}-4by-1+4{{b}^{2}}=0\)恰有三条公切线，若\(a\in R\)，\(b\in R\)且\(ab\ne 0\)，则\(\dfrac{1}{{{a}^{2}}}+\dfrac{1}{{{b}^{2}}}\)的最小值为_____________．

\((4)\)对于函数\(f\left( x \right)\)，如果\(f\left( x \right)\)可导，且\(f\left( x \right)={f}{{'}}\left( x \right)\)有实数根\(x\)，则称\(x\)是函数\(f\left( x \right)\)的驻点\(.\)若函数\(g\left( x \right)={{x}^{2}}\left( x > 0 \right),h\left( x \right)=\ln x,\varphi \left( x \right)=\sin x\left( 0 < x < \pi \right)\)的驻点分别是\({{x}_{1}},{{x}_{2}},{{x}_{3}}\)，则的大小关系是______\((\)用“\( < \)”连接\().\)   

\((1).\)双曲线的两条渐近线互相垂直，则离心率\(e=\_\_\_\_\_\)．

\((2).\)观察下列等式：  

\(1=1\)

\(2+3+4=9\)

\(3+4+5+6+7=25\)

\(4+5+6+7+8+9+10=49\)

照此规律第\(n\)个等式为______________________．

\((3).\)复数\(z= \dfrac{2}{1-i} \)给出四个结论：\(①\left| z \right|=2\)；\(②{{z}^{2}}=2i\)；\(③\overline{z}=-1+i\)；\(④z的虚部为i \)，正确的有__________\((\)填序号\()\)

\((4).\)若数列\(\left\{ {{a}_{n}} \right\}n\in N+\)是等差数列，则数列\({{b}_{n}}=\dfrac{{{a}_{1}}+{{a}_{2}}+\cdots {{a}_{n}}}{n}\)，也是等差数列，类比上述性质，相应地有：若数列\(\left\{ {{C}_{n}} \right\}n\in N+\)是等比数列，且\({{C}_{n}} > 0\)，则数列\({{d}_{n}}=\)____________也是等比数列．

已知\(i\)是虚数单位，复数\(z=(1+i)·i^{3}\)，则 \(\dfrac{1}{z}\) 的共轭复数是(    )

\((1)\)计算\({\log }_{2.5}6.25+\lg ⁡ \dfrac{1}{100}+\ln ⁡ \sqrt{e}+{2}^{1+{\log }_{2}3} =\)______．

\((2){{\left( \sqrt{x}-\dfrac{i}{x} \right)}^{8}}\)的二项展开式中，含\(x\)的一次项的系数为         \(.(\)用数字作答\()\)

\((3)\)两圆\({{x}^{2}}+{{y}^{2}}+2ax+{{a}^{2}}-4=0\)和\({{x}^{2}}+{{y}^{2}}-4by-1+4{{b}^{2}}=0\)恰有三条公切线，若\(a\in R\)，\(b\in R\)且\(ab\ne 0\)，则\(\dfrac{1}{{{a}^{2}}}+\dfrac{1}{{{b}^{2}}}\)的最小值为_____________．

\((4)\)若函数\(f\left( x \right)\)满足\(f\left( x-1 \right)=\dfrac{1}{f\left( x \right)-1}\)，当\(x\in \left[ -1,0 \right]\)时，\(f\left( x \right)=x\)，若在区间\(\left[ -1,1 \right]\)上，\(g\left( x \right)=f\left( x \right)-mx+m\)有两个零点，则实数\(m\)的取值范围为           ．