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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2000

  • question_answer
    The curve represented by\[\operatorname{Im}({{z}^{2}})=K,\]where K is a non-zero real number is:

    A)  a pair of straight lines

    B)  an ellipse

    C)  a parabola

    D)  a hyperbola

    Correct Answer: D

    Solution :

    Let \[z=x+iy\]then \[{{z}^{2}}={{x}^{2}}-{{y}^{2}}+2ixy\] \[\therefore \] \[\operatorname{Im}({{z}^{2}})=K\Rightarrow 2xy=K\Rightarrow xy=K/2\]which is a hyperbola.


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