11th Class Mathematics Complex Numbers and Quadratic Equations Question Bank Critical Thinking

  • question_answer If \[z\] is a complex number, then the minimum value of \[|z|+|z-1|\] is [Roorkee 1992]

    A) 1

    B) 0

    C) 1/2

    D) None of these

    Correct Answer: A

    Solution :

    First note that \[|-z|\,=\,|z|\] and \[|{{z}_{1}}+{{z}_{2}}|\,\le \,|{{z}_{1}}|+|{{z}_{2}}|\] Now \[|z|+|z-1|\,=\,|z|+|1-z|\,\ge \,|z+(1-z)|\,=\,|1|=1\] Hence, minimum value of\[|z|+|z-1|\]is 1.

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