Solved papers for JEE Main & Advanced AIEEE Solved Paper-2003

done AIEEE Solved Paper-2003 Total Questions - 3

• question_answer1) Let \[{{z}_{1}}\] and \[{{z}_{2}}\] be two roots of the equation \[{{z}_{2}}+az+b=0,\,\,z\] being complex. Further, assume that the origin, \[{{z}_{1}}\] and \[{{z}_{2}}\] form an equilateral triangle. Then,     AIEEE  Solved  Paper-2003
  A)
                                          \[{{a}^{2}}=b\]                                 
  done clear
  B)
  \[{{a}^{2}}=2b\]               
  done clear
  C)
                        \[{{a}^{2}}=3b\]           
  done clear
  D)
                        \[{{a}^{2}}=4b\]
  done clear
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• question_answer2) If z and \[\omega \] are two non-zero complex numbers  such  that  \[\left| z\,\omega  \right|=1\] and arg (z) - arg \[(\omega )=\frac{\pi }{2}\], then \[\overline{z}\omega \] is equal to     AIEEE  Solved  Paper-2003    
  A)
                          1                             
  done clear
  B)
  -1           
  done clear
  C)
  \[i\]                                       
  done clear
  D)
  \[-i\]
  done clear
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• question_answer3) If \[{{\left( \frac{1+i}{1-i} \right)}^{x}}=1\] , then             AIEEE  Solved  Paper-2003   
  A)
  \[x=4\,n\], where n is any positive integer
  done clear
  B)
  \[x=2\,n\], where n is any positive integer
  done clear
  C)
  \[x=4\,n+1\], where n is any positive integer
  done clear
  D)
  \[x=2\,n+1\], where n is any positive integer
  done clear
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