if `(z+1/z) = 3` then find the value of `(z^2+1/z^2)`

If z + z^(-1)= 1 , then find the value of z^(100) + z^(-100) .

If z_1, z_2, z_3 are distinct nonzero complex numbers and a ,b , c in R^+ such that a/(|z_1-z_2|)=b/(|z_2-z_3|)=c/(|z_3-z_1|) Then find the value of (a^2)/(z_1-z_2)+(b^2)/(z_2-z_3)+(c^2)/(z_3-z_1)

If z_(1)=2-i, z_(2)=1+ 2i, then find the value of the following : (i) Re((z_(1)*z_(2))/(bar(z)_(2))) (ii) Im (z_(1)*bar(z)_(2))

If z^(2)+z+1=0 then the value of (z+1/z)^(2)+(z^(2)+1/z^(2))^(2)+(z^(3)+1/z^(3))^(2)+....+(z^(21)+1/z^(21))^(2) is equal to

It is given that complex numbers z_1 and z_2 satisfy |z_1|=2 and |z_2|=3. If the included angled of their corresponding vectors is 60^0 , then find the value of |(z_1+z_2)/(z_1-z_2)| .

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

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

If |z_1|=1,|z_2|=2,|z_3|=3,a n d|9z_1z_2+4z_1z_3+z_2z_3|=12 , then find the value of |z_1+z_2+z_3|dot

If |z_1|=1,|z_2|=2,|z_3|=3,a n d|9z_1z_2+4z_1z_3+z_2z_3|=12 , then find the value of |z_1+z_2+z_3|dot