If `z_1` is a root of the equation `a_0z^n+a_1z^(n-1)+........+(a_(n-1)z+a_n=3,` where `|a_1| lt 2` for `i=0,1,.....n,` then (a). `|z|=3/2` (b). `|z| lt 1/4` (c). `|z| gt 1/4` (d). `|z| lt 1/3`

zo is one of the roots of the equation z^(n)cos theta0+z^(n-1)cos theta2+......+z cos theta(n-1)+cos theta(n)=2, where theta in R, then (A)|z0| (1)/(2)(C)|z0|=(1)/(2)

If z_(1),z_(2),z_(3),z_(4) are roots of the equation a_(0)z^(4)+a_(1)z^(3)+a_(2)z^(2)+a_(3)z+a_(4)=0, where a_(0),a_(1),a_(2),a_(3) and a_(4) are real,then

Prove that none of the roots of the equation z^(n) = 2(1+ z+z^2 + …...+ z^(n-1)), n gt 1 , lies outside the circle |z|=3 .

If 2+z+z^4=0, where z is a complex number then (A) 1/2 lt|z|lt1 (B) 1/2lt|z|lt1/3 (C) |z|ge1 (D) none of these

If z_(1),z_(2),z_(3),…,z_(n-1) are the roots of the equation z^(n-1)+z^(n-2)+z^(n-3)+…+z+1=0 , where n in N, n gt 2 and omega is the cube root of unity, then

If z is a complex number satisfying z+z^(-1)=1 then z^(n)+z^(-n),n in N, has the value

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

If |a_(k)|<3,1<=k<=n, then all complex numbers z satisfying equation 1+a_(1)z+a_(2)z^(2)+.........+a_(n)z^(n)=0

z0is a root of the equation z^(n)cos[theta o]+z^(n-1)cos[theta1]+z^(n-2)cos theta[theta2]+......+z^(n)cos[theta[n-1]]+cos theta[n]=2 where Theta[i]in R

If n is a natural number gt 2 , such that z^(n) = (z+1)^(n) , then