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 f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is (a)(|z|)/2 (b) |z| (c) 2|z| (d) none of these

If z=-2 + 2 sqrt3i then z^(2n) + z^(n) + 2^(4n) may be equal to

If A=[cos theta-sin theta sin theta cos theta], then A^(T)+A=I_(2), if theta=n pi,n in Z(b)theta=(2n+1)(pi)/(2),quad n in Z(c)theta=2n pi+(pi)/(3),quad n in Z(d) none of these

If z=cos theta+i sin theta, then the value of (z^(2n)-1)/(z^(2n)+1)(A)i tan n theta(B)tan n theta(C)i cot n theta(D)-i tan n theta

If n in Z , then (2^(n))/(1+i)^(2n)+(1+i)^(2n)/(2^(n)) is equal to

If i=sqrt(-1) , then {i^(n)+i^(-n), n in Z} is equal to

If n is a positive integer but not a multiple of 3 and z=-1+i sqrt(3), then (z^(2n)+2^(n)z^(n)+2^(2n)) is equal to

Which of the following is true for z=(3+2i sin theta)(1-2sin theta)wherei=sqrt(-1)?( a) z is purely real for theta=n pi+-(pi)/(3),n in Z (b)z is purely imaginary for theta=n pi+-(pi)/(2),n in Z(c)z is purely real for theta=n pi,n in Z(d) none of these

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+sqrt(2)|z+1|+i=0 , then z= (A) 2+i (B) 2-i (C) -2-i (D) -2+i