" If "|Z-3|=3," then "(Z-6)/(Z)=

If |z-3|=3, then show that (z-6)/(z)=i tan(arg z)

If |z-3|=3, then show that (z-6)/(z)=i tan(arg z)

z_(1), z_(3), and z_(3) are complex numbers such that z_(1) + z_(2) + z_(3)=0 and |z_(1)| = |z_(2)| = |z_(3)| = 1 then z_(1)^(2)+z_(2)^(2)+z_(3)^(3)

Z_(1), Z_(2),......,Z_(6) are non-zero complex number such that (Z_(1))/(Z_(2))+(Z_(3))/(Z_(4))+(Z_(5))/(Z_(6))=a+bi, where a,b real and (Z_(2))/(Z_(1))+(Z_(4))/(Z_(3))+(Z_(6))/(Z_(5))=0 then ((Z_(2))/(Z_(2)))^(2)+((Z_(3))/(Z_(4)))^(2)+((Z_(5))/(Z_(6)))^(2) =

If z^(n) = cos"" (n pi)/(3) + isin"" (n pi)/(3), then z_(1), z_(2) …. Z_(6) is

If |z_(1)|=1,|z_(2)|=2,|z_(3)|=3 ,then |z_(1)+z_(2)+z_(3)|^(2)+|-z_(1)+z_(2)+z_(3)|^(2)+|z_(1)-z_(2)+z_(3)|^(2)+|z_(1)+z_(2)-z_(3)|^(2) is equal to

bb"statement-1" " Let " z_(1),z_(2) " and " z_(3) be htree complex numbers, such that abs(3z_(1)+1)=abs(3z_(2)+1)=abs(3z_(3)+1) " and " 1+z_(1)+z_(2)+z_(3)=0, " then " z_(1),z_(2),z_(3) will represent vertices of an equilateral triangle on the complex plane. bb"statement-2" z_(1),z_(2),z_(3) represent vertices of an triangle, if z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)=0