341how do you know that RHS is not real? esp since nishant sir has indicated that z1/z2 is real
If z1 and z2 be two distict complex numbers such that z_1+z_2=\frac{z_1}{\left|z_2 \right|^{2}}+\frac{z_2}{\left|z_1 \right|^{2}}
then prove that 1+\left|z_1 \right|\left|z _2 \right|=\frac{z_1}{z_2}+\frac{z_2}{z_1}
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8 Answers
62z_1(1-1/|z_2^2|)=-z_2(1-1/|z_1^2|)
Thus Z1 adn Z2 are parallel (or antiparallel)
I hope this helps!
39sir i have a doubt in what ever we have to prove
the LHS is a real quantity and RHS is not.
so how both of them can be equated???
34162@bhargav.. iin such cases the only solution is when both sides are zero..
(not to say that that is the case here)
11I've been able to prov e that z1 & z2can't be anti-parallel.....they have to be parallel...
11Continuing from where I left last night, z1=keiθ
z2=leiθ
Putting them in the given eqn we have 1k+1l=k+l, from which we have kl=1....
Let k<1 and l>1.....
but if that's the case then R.T.P requires both k and l to be equal....
But that's not possible as both z1 & z2 are distinct.......So eureka - just check ur qsn once...[99]
