IIT JEE , AIEEE Forum - Mathematics , Algebra

sneha.bagri

the inequality $\begin{vmatrix}z-2\end{vmatrix}$ > $\begin{vmatrix}z-4\end{vmatrix}$ represents the given region by

a.Re z>2

b.Re z<0

c.Re z>3

Re z>0

plz giv ur xplanations....

oneyeartogo

The ans is c Re z>3

$(z - 2) (z' - 2) > (z - 4) (z' - 4)\\on\: opening\: and\:simplifying\: we\;get:\\=>(z+z') > 6\:\:\;\:\;\;\:\:\:\:\:\:\:\:\:\:\:\;\:\:\:\:\:\;\;\;\;\:\:\:\;\:\:\;\;\;\;\;\;\:\:\\=>2 re(z) > 6\:\:\;\:\;\;\:\:\:\:\:\:\:\:\:\:\:\;\:\:\:\:\:\;\;\;\;\:\:\:\;\:\:\;\;\;\;\;\;\:\:\\=>re(z) > 3\:\:\;\:\;\;\:\:\:\:\:\:\:\:\:\:\:\;\:\:\:\:\:\;\;\;\;\:\:\:\;\:\:\;\;\;\;\;\;\:\:\\Note:\;z'\;refers\;to\;z\:bar\:\:\;\:\;\;\:\:\:\:\:\:\:\:\:\:\:\;\:\:\:\:\:\;\;\;$

priyesh

simple yaar

the inequality means distance of point from (2,0) should be greater than (4,0)

clearly this will happen when x>3 i.e re(z) > 3

animal

a simple shortcut is also there for mcq

u can draw the 2 circles represented by the 2 eqns and can apply the inequality there and we can see

graphically that it is true for re>3.

hope u got it.

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