# 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

Staff Emeritus
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. :)