A complex problem

1. Nov 26, 2006

nighthelios

it's ic a problem on comlex numbers
IF z1 ,z2 ,z3 are vertices of equilateral triangle in argand plane
then
P.T.
z1*z1 + z2*z2 =z1*z2
i hav 1 soln but it's not tat satisfactory

2. Nov 26, 2006

AKG

Why doesn't z3 appear anywhere in the equation you're trying to prove?

3. Nov 27, 2006

nighthelios

cos we hav to eliminate z3

4. Nov 27, 2006

AKG

No, it's because either you wrote the question wrong or the question given to you was stated wrong. What you've asked to prove is impossible to prove, because it's false in general.

5. Nov 27, 2006

HallsofIvy

One example would be to take the vertices of the equilateral triangle to be the cube roots of 1: 1, $-\frac{1}{2}+i\frac{\sqrt{3}}{2}$, and $-\frac{1}{2}-i\frac{\sqrt{3}}{2}$. If we take z1= 1, z2= $-\frac{1}{2}+i\frac{\sqrt{3}}{2}$, then z12+ z22= $\frac{1}{2}-i\frac{\sqrt{3}}{2}$ which is not z1z2!

Go back and check exactly what it is you are asked to prove.

6. Nov 27, 2006

AKG

Or take z1 = 0, z2 = anything else, and z3 any of the two points in the plane that would make z1, z2, z3 an equilateral triangle.