question_answer

If \[{{Z}_{1}}=a+i\,b\] and \[{{Z}_{2}}=c+i\,d\] are complex numbers such that \[\left| {{Z}_{1}} \right|=\left| {{Z}_{2}} \right|=1\] and \[\operatorname{Re}({{Z}_{1}}\overline{{{Z}_{2}}})=0,\] then the pair of complex numbers \[a+i\,c={{w}_{1}}\] and \[b+i\,d={{w}_{1}}\] satisfies ____.

A)  \[|{{w}_{1}}|\,\ne 0\]             

B)  \[|{{w}_{2}}|\,\ne 1\]

C)  \[\operatorname{Re}({{w}_{1}}{{\overline{w}}_{2}})=0\]         

D)  All the above

E)  None of these