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VIT Engineering VIT Engineering Solved Paper-2015

  • question_answer
    If the complex number z lies on a circle with centre at the origin and radius \[\frac{1}{4},\] then the complex number \[-1+8z\] lies on a circle with radius

    A) 4                                             

    B) 1

    C) 3                                             

    D) 2

    Correct Answer: D

    Solution :

    Given,  \[|z|=\frac{1}{4}\] Let             \[z'=-1+8z\] \[\Rightarrow \]             \[z=\frac{z'+1}{8}\] \[\Rightarrow \]              \[|z|=\frac{|z'+1|}{8}\] \[\Rightarrow \]              \[\frac{1}{4}=\frac{|z'+1|}{8}\] \[\Rightarrow \]               |z? + 1| = 2 Hence, z? lies on a circle with centre (-1, 0) and radius 2.


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