If \[{{z}_{1}}=a+ib\] and \[{{z}_{2}}=c+id\] are complex numbers such – McqOptions

MCQOPTIONS

1.	If \[{{z}_{1}}=a+ib\] and \[{{z}_{2}}=c+id\] are complex numbers such that \[\|{{z}_{1}}\|\,=\,\|{{z}_{2}}\|=1\] and \[R({{z}_{1}}\overline{{{z}_{2}}})=0,\] then the pair of complex numbers \[{{w}_{1}}=a+ic\] and \[{{w}_{2}}=b+id\] satisfies [IIT 1985]
A.	\[\|{{w}_{1}}\|=1\]
B.	\[\|{{w}_{2}}\|=1\]
C.	\[R({{w}_{1}}\overline{{{w}_{2}}})=0,\]
D.	All the above
Answer» E.

Discussion

No Comment Found

Related MCQs

If \[z\] is a complex number, then the minimum value of \[|z|+|z-1|\] is [Roorkee 1992]
If \[{{S}_{1}},\ {{S}_{2}},\ {{S}_{3}},...........{{S}_{m}}\] are the sums of \[n\] terms of \[m\] A.P.'s whose first terms are \[1,\ 2,\ 3,\ ...............,m\] and common differences are \[1,\ 3,\ 5,\ ...........2m-1\] respectively, then \[{{S}_{1}}+{{S}_{2}}+{{S}_{3}}+.......{{S}_{m}}=\]
If the roots of the equation \[q{{x}^{2}}+px+q=0\]where p, q are real, be complex, then the roots of the equation \[{{x}^{2}}-4qx+{{p}^{2}}=0\] are
The sum of the series\[\frac{4}{1\,!}+\frac{11}{2\,!}+\frac{22}{3\,!}+\frac{37}{4\,!}+\frac{56}{5\,!}+...\]is [Kurukshetra CEE 2002]
The centre of the circle passing through the point (0, 1) and touching the curve \[y={{x}^{2}}\]at (2, 4) is [IIT 1983]
If \[(1+i)(1+2i)(1+3i).....(1+ni)=a+ib\], then 2.5.10....\[(1+{{n}^{2}})\] is equal to [Karnataka CET 2002; Kerala (Engg.) 2002]
Let \[{{S}_{1}},\ {{S}_{2}},.......\]be squares such that for each \[n\ge 1\], the length of a side of \[{{S}_{n}}\] equals the length of a diagonal of \[{{S}_{n+1}}\]. If the length of a side of \[{{S}_{1}}\]is\[10cm\], then for which of the following values of \[n\] is the area of \[{{S}_{n}}\] less then \[1\ sq\ cm\] [IIT 1999]
If \[a
If \[S=\sum\limits_{n=0}^{\infty }{\frac{{{(\log x)}^{2n}}}{(2n)\,!},}\] then \[S\] =
If \[x\]is real and \[k=\frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1},\] then [MNR 1992; RPET 1997]