共50条信息
若\(z=\sin \theta -\dfrac{3}{5}+(\cos \theta -\dfrac{4}{5})i\)是纯虚数,则\(\tan (\theta -\dfrac{\pi }{4})\)的值为\((\) \()\)
已知\(z=a+bi(a,b∈R)\),当\(a=0\)时,复数\(z\)为纯虚数\(.\)( )
判断\((\)正确的打“\(√\)”,错误的打“\(×\)”\()\)
\((1)\)若\(a\),\(b\)为实数,则\(z=a+bi\)为虚数\(.\) \((\) \()\)
\((2)\)复数\(z=3i\),\(z_{2}=2i\),则\(z_{1} > z_{2}.\) \((\) \()\)
\((3)\)复数\(z=bi\)是纯虚数\(.\) \((\) \()\)
\((4)\)实数集与复数集的交集是实数集\(.\) \((\) \()\)
下列命题中,错误命题的序号是____________.
\(①\)两个复数不能比较大小;\(②z_{1}\),\(z_{2}\),\(z_{3}∈C\),若\((z_{1}-z_{2})^{2}+(z_{2}-z_{3})^{2}=0\),则\(z_{1}=z_{3}\);
\(③\)若\((x^{2}-1)+(x^{2}+3x+2)i\)是纯虚数,则实数\(x=±1\);\(④z\)是虚数的一个充要条件是\(z+\overset{\_}{{z}}\,∈R\).
复数\(\dfrac{5i}{1{+}2i}\)的虚部是\(({ })\)
复数\(z=2-3i\)的虚部为
下面四个式子中,正确的是 ( )
\(.\)已知复数\(z=(\cos θ-i\sin θ)(1+i)\),则“\(z\)为纯虚数”的一个充分不必要条件是( )
设\(z\)是虚数,\(w=z+ \dfrac{1}{z} \)是实数,且\(-1 < w < 2\)
\((1)\)求\(\left|z\right| \)的值及\(z\)的实部的取值范围.
\((2)\)设\(μ= \dfrac{1-z}{1+z} \),求\(w-{μ}^{2} \)的最小值.
\(i\)为虚数单位,若关于\(x\)的方程\({x}^{2}-(2+i)x+1+mi=0(m∈R) \)有一实根为\(n\),则\(m=\) ________.
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