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_i| lt 2` for `i=0,1,.....n,` then (a). `|z|=3/2` (b). `|z| lt 1/4` (c). `|z| gt 1/4` (d). `|z| > 1/3`

If z_1 is a root of the equation a_0z^n+a_1z^(n-1)++a_(n-1)z+a_n=3,w h e r e|a_i| 1/4 d. |z|<1/3

zo is one of the roots of the equation z^n cos theta_0+ z^(n-1) cos theta_2 +. . . . . . + z cos theta_(n-1) + cos theta_(n) = 2 , where theta in R , then (A) |z_0| lt 1/2 (B) |z_0| gt 1/2 (C) |z_0| = 1/2 (D)None of these

If 8i z^3+12 z^2-18 z+27 i=0,t h e n |z|=3/2 b. |z|=2/3 c. |z|=1 d. |z|=3/4

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_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 Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. I-(2^n-1)Z d. none of these

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

If z is complex number such that |(6z-i)/(2+3i z)|lt=1 , then which of the following can be possible? (a) |z|=1/2 (b) |z|=1/3 (c) |z|=1 (d) |z|=1/4

if z_(1) = 3i and z_(2) =1 + 2i , then find z_(1)z_(2) -z_(1)