SOLUTION: If z1+z2+z3=0 and z1^2+z2^2+z3^2=0, prove that |z1|=|z2|=|z3|

Algebra.Com
Question 888022: If z1+z2+z3=0 and z1^2+z2^2+z3^2=0, prove that |z1|=|z2|=|z3|
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!




Substitute in











































by symmetry, we may swap  and 





Edwin
RELATED QUESTIONS

If z1+z2+z3=0 and z1^2+z2^2+z3^2=0, prove that... (answered by Edwin McCravy)
if z1,z2,z3, are the vertices of equilateral triangle then show that... (answered by venugopalramana)
prove |z1 + z2+... (answered by richwmiller)
z1=2+i z2=-3+i... (answered by Edwin McCravy)
show that... (answered by ikleyn)
prove that if z1 z2 z3 are complex numbers on the unit circle such that z1+z2+z3=0, then... (answered by greenestamps)
Three complex numbers z1,z2,z3 are such that z1+z2+z3=0 and |z1|=|z2|=|z3|.prove that... (answered by ikleyn)
Z1=3e^i180/3 Z2=2e^i4*180/3 Z3=z1z2 Z1= -0.5 +0.866i Z2=z1^3 Z1= -16... (answered by Alan3354)
given that z1=2+i and z2=-3+4i and 1/z3=1/z1+1/z2. determine the value of z3 in standard... (answered by mananth,Edwin McCravy,math_tutor2020)