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  • For a complex number z, the minimum value of |z|+|z-2i| is

For a complex number z, the minimum value of |z|+|z-2i| is

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Solution: We have ,

For zepsilon R

left | 2i ight |=left | z+(2i-z) ight |leq left | z ight |+left | 2i-z ight |\ \Rightarrow 2leq left | z ight |+left | z-2i ight |

Thus minimum value of left | z ight |+left | z-2i ight | is 2 andit is attained when z=i

Posted by

Deependra Verma

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