" 2.(1) If "z=3-5i" ,then show that "z^(3)-10z^(2)+58z-136=0

If z=3-5i Show that z^(3)-10z^(2)+58z-136=0

if iz^3+z^2-z+i=0 then show that absz=1

If iz^3+z^2-z+i = 0 , then show that |z|=1.

If iz^(3)+z^(2)-z+i=0 then show that |z|=1.

If z = 3- 5i then z^(2) - 10z + 30=

If z_(1)=-3+4i and z_(2)=12-5i, "show that", |z_(1)z_(2)|=|z_(1)||z_(2)|

If the complex numbers z_(1),z_(2),z_(3) represents the vertices of an equilaterla triangle such that |z_(1)|=|z_(2)|=|z_(3)| , show that z_(1)+z_(2)+z_(3)=0

If |z_(1)|=|z_(2)|=....|z_(n)|=1 , then show that, |z_(1)+z_(2)+z_(3)+....z_(n)|= |(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))+...+(1)/(z_(n))|

Show that if iz^(3)+z^(2)-z+i=0, then |z|=1

If z_(1) = 3, z_(2) = -7i, and z_(3) = 5 + 4i, show that (z_(1) + z_(2)) z_(3) = z_(1) z_(3) + z_(2) z_(3)