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For any complex number z, |z|+|z+z-2i| will not exceed___________?

For any complex number z, |z|+|z+z-2i| will not exceed___________?

Grade:

2 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

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).

NARAYANA SARMA
19 Points
10 years ago

then the minimum value will be_______________________?

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