Equilateral Triangle Complex Numbers Problem

[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 have 1 soln but it's not tat satisfactory

 

[AKG]

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 have 1 soln but it's not tat satisfactory

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

 

[nighthelios]

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

cos we have to eliminate z3

 

[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.

 

[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.

 

[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.