Q.

For any complex number z, the minimum value of |z|+|z−2i| is

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a

0

b

1

c

2

d

none of these

answer is C.

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Detailed Solution

We have, for  z∈C|2i|=|z+(2i−z)|≤|z|+|2i−z|⇒2≤|z|+|z−2i|Thus, minimum value of |z|+|z−2i|  is 2 and it is attained when z =i.
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For any complex number z, the minimum value of |z|+|z−2i| is