2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced JEE Main Paper (Held On 19 May 2012)

  • question_answer
    Let Z and? F be complex numbers such that \[|Z|=|W|,\] and arg Z denotes the principal argument of Z. Statement 1. If arg Z+ arg \[W=\pi ,\]then \[Z=-\overline{W}.\] Statement1: \[|Z|=|W|,\]implies arg Z- arg \[\overline{W}=\pi .\]     JEE Main  Online Paper (Held On 19  May  2012)

    A) Statement 1 is true. Statement 2 is false. Statement 1 is true, Statement 2 is true,

    B)                        Statement 2 is a correct explanation for Statement 1.

    C)                        Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

    D)                        Statement 1 is false, Statement 2 is true.

    Correct Answer: A

    Solution :

                    Let\[|Z|=|W|=r\] \[\Rightarrow \]\[Z=r{{e}^{i\theta }},W=r{{e}^{i\phi }}\]where\[\theta +\phi =\pi \] \[\therefore \]\[\overline{W}=r{{e}^{-i\phi }}\] Now,\[Z=r{{e}^{i(\pi -\phi )}}=r{{e}^{i\pi }}\times {{e}^{-i\phi }}=-r{{e}^{-i\phi }}\]\[=-\overline{W}\] Thus, statement-1 is true but Statement-2 is false.


You need to login to perform this action.
You will be redirected in 3 sec spinner