SOLUTION: Verify that sqrt2|z|≤|Re(z)|+|Im(z)|

Question 1144069: Verify that sqrt2|z|≤|Re(z)|+|Im(z)|
Answer by ikleyn(52915) (Show Source): You can put this solution on YOUR website!
.


Hello, I do understand what is written in the right side of this inequality.


    > > >  But I do not understand what is written in its left side.  < < <



If it is  

     sqrt(2) * |z| <= |Re(z)| + |Im(z)|,      (1)

then I can easily disprove it:  take  z = 1 = 1 + 0*i;

                                Then  sqrt(2) * |z| = sqrt(2) in the left side 

                                and  |Re(z)| + |Im(z)| = 1 + 0 = 1,

                                so the inequality (1) is not correct in this case.



If it is  

     sqrt((2)*|z|) <= |Re(z)| + |Im(z)|,      (2)

then I can easily disprove it, again:  

                                take  z = 1 = 1 + 0*i;

                                Then  sqrt((2) * |z|) = sqrt(2) in the left side 

                                and  |Re(z)| + |Im(z)| = 1 + 0 = 1 in the right side,

                                so the inequality (2) is not correct in this case, too.

Could you PLEASE write your post / posts more ACCURATELY, in a way the tutors do not spend their time for NOTHING,
trying to guess and/or decipher your writing ?

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