Complex numbers

1. Nov 29, 2011

Macarenses

How does one prove that for w≠+-1 , w a complex number, there are exactly 2 solutions to the equation w=0.5(z+1/z)? i'm at a total loss here. Could someone clue me in on this one?

2. Nov 29, 2011

ramsey2879

What if you multiplied each side by 2z?

Last edited: Nov 29, 2011
3. Nov 30, 2011

HallsofIvy

The best way to prove there are two solutions is to find them! That is what ramsey2879 is suggesting.

4. Nov 30, 2011

ramsey2879

I do believe that the quadratic formula will work for equations with complex coefficients even if it is not clear (at least to me) how to find the square root of a complex number. Just write the solution out in the radical form simplified as far as posible.

5. Dec 1, 2011

lostcauses10x

Do a internet search: complex numbers solve square root

6. Dec 2, 2011

TheBonobo4

w=0.5(z+1/z)
w=0.5z+0.5/z
wz=0.5z^2+0.5
0.5z^2+0.5-wz=0

If you could substitute a value of either w or z you could work out the other using Quadratic Formula

x = (-b +- sqrt(b^2-4ac))/2a

Other than this, I can't see how you solve it since you have 2 unknowns. Either way you have a squared value for z so z has 2 solutions.

Sorry if I was no help, this is my first post here as I just joined today. :)