Maximum Value of |Z| if |Z+4/Z | = 3

Question

anonymous · Answer

i used this relation |Z1+Z2| < = |Z1| + |Z2| ...But my Result is wrong..:_

shubhamsrg · Answer

your attempt seems fine.
can you show your work ?

anonymous · Answer

Finally after Solving i Got an Equation like this

|Z|^2 - 3|Z| + 4 > = 0

shubhamsrg · Answer

these seems to be always > 0 ?

shubhamsrg · Answer

it should have a minimum value then
unless some mistake ?

anonymous · Answer

Sorry.....Did nt get u....

anonymous · Answer

i think u mean it shuld be    < = 0 for maximum ryt ?

shubhamsrg · Answer

the given quadratic eqn can not be simplified.
it must be a parabola with mouth open upwards
such parabolas have minimum vale

shubhamsrg · Answer

value*

anonymous · Answer

So..Hw can We approach this ?

shubhamsrg · Answer

|Z+4/Z | <= |z| + 4/|z|
3  <= |z| + 4/|z|

|z|^2 - 3|z| + 4 >=0 
hmm
this is always greater than 0 for any value of |z|
you should be asking minimum value of |z| ?

anonymous · Answer

there are no real values for which $$\left|z+{4\over z}\right|=3$$

anonymous · Answer

$$
|z|^2+8+{16\over|z|^2}=9\
|z|^4-|z|^2+16=0
$$

anonymous · Answer

the solution for this system says that the "z" is a complex number