As #z_1# and #z_2# are solutions of#z^2-az+b=0#,
we have #z_1+z_2=a# and #z_1*z_2=b#.
If #z_1# and #z_2# have same arguement then we can say #z_2=kz_1#, where #k# is a real number.
As #a=z_1+z_2=(k+1)z_1#, #argz_1=argz_2=arga# and
as #b=z_1*z_2#, #argb=argz_1+argz_2=2arga#
As #a,b,z# are complex, we must have discriminant #Delta<0#. Here discriminant is given #Delta=|a|^2-4|b|*1<0#. (see @note below)
or #|a|^2-4|b|<0#
@Note - Discriminant for quadratic equation #lx^2+mx+n=0# is #m^2-4ln#. Here #a,b,z# are complex but in complex numbers, you cannot compare numbers like that and you have #|m|^2-4|l||n|<0#
