共50条信息
对于复数\(z=a+bi(a,b\in R)\),若\(z+i=\dfrac{2-i}{1+2i}\),则\(b=\)_________.
已知\(i\)为虚数单位,若\(\dfrac{1+i}{1-i}=a+bi(a,b\in R)\),则\(a+b=(\) \()\)
已知\( \dfrac{m}{1-i}=1-ni, \)其中\(m,n \)是实数,\(i \)是虚数单位,则\(m+n=\)
已知 \(i\) 是虚数单位,若\( \dfrac{1+7i}{2-i}=a+bi\;\left(a,b∈R\right) \)则 \(ab\)的值是( )
已知关于实数\(x\),\(y\)的方程组\(\begin{cases}\left(2x-1\right)+i=y-\left(3-y\right)i,① \\ \left(2x+ay\right)-\left(4x-y+b\right)i=9-8i②\end{cases} \),有实数解,求实数\(a\),\(b\)的值.
设\(x\),\(y∈R\),若\((x+y)+(y-1)i=(2x+3y)+(2y+1)i\),则复数\(z=x+yi\)在复平面上对应的点位于( )
已知\(z∈C\),且\(z= \dfrac{1+ti}{1-ti}(t∈R)\),则复数\(z\)对应的点的轨迹为____________.
实数\(x\),\(y\)满足\(z\)\(=\)\(y\)\(+\)\(x\)\(i\),\(z\)\({\,\!}_{2}=\)\(y\)\(i-\)\(x\),且\(z\)\({\,\!}_{1}-\)\(z\)\({\,\!}_{2}=2\),则\(xy\)的值是( )
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