If `|z_1|=|z_2|=dot=|z_n|=1,` prove that `|z_1+z_2+z_3++z_n|=1/(z_1)+1/(z_2)+1/(z_3)++1/(z_n)dot`

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

If |z_1|=1,|z_2|=1 then prove that |z_1+z_2|^2+|z_1-z_2|^2 =4.

If |z_1+z_2| = |z_1-z_2| , prove that amp z_1 - amp z_2 = pi/2 .

If |z_1|=|z_2|=.=|z_n|=1, then the value of |z_1+z_2+z_3+..+z_n| is equal to (A) 1 (B) |z_1|+|z_2|+z_3|+…..+|z_n| (C) |1/z_1+1/z_2+1/z_3+……….+1/z_n| (D) n

Prove that |z_1+z_2|^2+|z_1-z_2|^2 =2|z_1|^2+2|z_2|^2 .

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

For any three complex numbers z_1, z_2 and z_3 , prove that z_1 lm (bar(z_2) z_3)+ z_2 lm (bar(z_3) z_1) + z_3lm(bar(z_1) z_2)=0 .

Prove that |1-barz_1z_2|^2-|z_1-z_2|^2=(1-|z_1|^2)(1-|z_2|^2) .