JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Conjugate, Modulus and Argument of complex number

  • question_answer
    The minimum value of  \[|2z-1|+|3z-2|\]is [RPET 1997]

    A) 0

    B) \[1/2\]

    C) \[1/3\]

    D) 2/3

    Correct Answer: C

    Solution :

    Given expression, \[|2z-1|+|3z-2|\],  minimum value of \[|2z-1|\]is 0 at \[z=\frac{1}{2}\]. So value of given expression \[=0+\frac{1}{2}=\frac{1}{2},\] minimum value of  \[|3z-2|\] is 0, at\[z=\frac{2}{3}\]. So value of given expression\[=\frac{1}{3}+0=\frac{1}{3}\]. So minimum value of given expression is\[\frac{1}{3}\].


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