If `z+1//z=2costheta,` prove that `|(z^(2n)-1)//(z^(2n)+1)|=|tanntheta|`

If z+1/z=2cos theta, prove that |(z^(2n)-1)/(z^(2n)+1)|=|tan n theta|

If z=costheta+isintheta , then (z^(2n)-1)/(z^(2n)+1)

If z=(costheta+isintheta) , show that z^(n)+(1)//(z^(n))=2cosntheta and z^(n)-(1)(z^(n))=2isinntheta

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

All the roots of equation z^n costgheta_0 +z^(n-1) costheta_1 +z^(n-2) costheta_2+…+costheta_n=2, when theta_0, theta_1, theta_2, ……theta_n epsilon R lie (A) on the line Re[(3+4i)z]=0 (B) inside the circel |z|=1/2 (C) outside the circle |z|= 1/2 (D) on the circle |z|= 1/2

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