If `z_n=[cos (pi/2)^(n/2)+i sin (pi/2)^(n/2)]` then `z_1.z_2.z_3…….oo`

If z_r=cos(pi/(3^r))+isin(pi/(3^r)),r=1,2,3, , prove that z_1z_2z_3 z_oo=idot

If z_(r)=cos((ralpha)/(n^(2)))+isin((ralpha)/(n^(2))),"where "r=1,2,3,...,nandi=sqrt(-1),"then. "lim_(n to oo) z_(1)z_(2)z_(3)...z_(n) is equal to

If z_1 = cos theta + i sin theta and 1,z_1,(z_1)^2,(z_1)^3,.....,(z_1)^(n-1) are vertices of a regular polygon such that (Im(z_1)^2)/(Re Z_1) = (sqrt5-1)/2 , then the value n is

If |z_(1)+z_(2)|^(2) = |z_(1)|^(2) +|z_(2)|^(2) " the " 6/pi amp (z_(1)/z_(2)) is equal to ……

Let arg(z_(k))=((2k+1)pi)/(n) where k=1,2,………n . If arg(z_(1),z_(2),z_(3),………….z_(n))=pi , then n must be of form (m in z)

If z_(1),z_(2),……………,z_(n) lie on the circle |z|=R , then |z_(1)+z_(2)+…………….+z_(n)|-R^(2)|1/z_(1)+1/z_(2)+…….+1/z-(n)| is equal to

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

Which of the following is not the general solution of 2^(cos2x)+1=3. 2^(-sin^2 x)? (a) npi,n in Z (b) (n+1/2)pi,n in Z (c) (n-1/2)pi,n in Z (d) none of these

if (2z-n)/(2z+n)=2i-1,n in N in N and IM(z)=10 , then

If z_1,z_2,z_3,………..z_(n-1) are the roots of the equation 1+z+z^2+…….+z^(n-1)=0, where n epsilon N, ngt2 then (A) z_1,z_2, …z_(n-1) are terms of a G.P. (B) z_1,z_2,……,z_(n-1) are terms of an A.P. (C) |z_1|=|z_2|=|z_3|=.|z_(n-1)|!=1 (D) none of these