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For any complex number z, |z|+|z+z-2i| will not exceed___________?
Hi Narayana,
The given expression is |z| + |2z-2i| = |z| + 2|z-i|
Now we know for any complex numbers z1 and z2, |z1-z2|≤|z1|+|z2|.
So |z-i| ≤ |z|+|i|
so |z-i|≤|z|+1.
So the given expression is ≤3|z|+2.
So the given expression will never exceed 3|z|+2.
Best Regards,
Ashwin (IIT Madras).
then the minimum value will be_______________________?
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