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

If |z_(1)|= |z_(2)|= ….= |z_(n)|=1 , prove that |z_(1) + z_(2) + …+ z_(n)|= |(1)/(z_(1)) + (1)/(z_(2)) + …(1)/(z_(n))|

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find the of z_(1)z_(2).

if z_(1),z_(2),z_(3),…..z_(n) are complex numbers such that |z_(1)|=|z_(2)| =….=|z_(n)| = |1/z_(1) +1/z_(2) + 1/z_(3) +….+1/z_(n)| =1 Then show that |z_(1) +z_(2) +z_(3) +……+z_(n)|=1

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1)z_(2)|= |z_(1)||z_(2)|

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1) + z_(2)| le |z_(1)| + |z_(2)|

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |(z_(1))/(z_(2))|= (|z_(1)|)/(|z_(2)|)

If z_(1),z_(2),z_(3) are three complex numbers, such that |z_(1)|=|z_(2)|=|z_(3)|=1 & z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0 then |z_(1)^(3)+z_(2)^(3)+z_(3)^(3)| is equal to _______. (not equal to 1)

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1)-z_(2)| gt |z_(1)|-|z_(2)|

If complex numbers z_(1)z_(2) and z_(3) are such that |z_(1)| = |z_(2)| = |z_(3)| , then prove that arg((z_(2))/(z_(1))) = arg ((z_(2) - z_(3))/(z_(1) - z_(3)))^(2) .

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1)z_(2) |= |z_(1)| |z_(2)|