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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-7

  • question_answer
    The principal value of the amplitude of \[\left( \mathbf{1}+\mathbf{i} \right)\]is:

    A) \[\frac{\pi }{4}\]                        

    B)  p              

    C)  \[\frac{\pi }{2}\]                                   

    D)  \[\frac{3\pi }{4}\]

    Correct Answer: A

    Solution :

    [a] \[\because z=1+i\] Here, \[x=1,y=1\] \[\therefore \tan \theta =\left( \frac{y}{x} \right)=\frac{1}{1}=1=\tan \frac{\pi }{4}\] \[\theta =\frac{\pi }{4}\] \[\because P\equiv \left( 1,1 \right)\]lies in 1st quadrant. \[\therefore \]The principal value of the amplitude\[z=\frac{\pi }{4}\]


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