If `|z-1|lt=2a n d|omegaz-1-omega^2|=a` where `omega` is cube root of unity , then complete set of values of `a` is `0lt=alt=2` b. `1/2lt=alt=(sqrt(3))/2` c. `(sqrt(3))/2-1/2lt=alt=1/2+(sqrt(3))/2` d. `0lt=alt=4`

If |z-1|<=2 and | omega z-1-omega^(2)|=a then (a) 0<=a<=2 (b) (1)/(2)<=a<=(sqrt(3))/(2) (c) (sqrt(3))/(2)-(1)/(2)<=a<=(1)/(2)+(sqrt(3))/(2)

If w is the cube root of unity then find the value ((-1+i sqrt(3))/(2))^(18)+((-1-i sqrt(3))/(2))^(18)

If w is a non real cube root of unity, then minimum value of | a+ bw + c w^2|is ( If a,b,c are not equal): (A) 0 (B) (sqrt3)/2 (C) 1 (D) 2

Discuss the extremum of f(x)={|x^2-2|,-1lt=x

If omega is a complex cube root of unity then the value of determinant |[2,2 omega,-omega^(2)],[1,1,1],[1,-1,0]|= a) 0 b) 1 c) -1 d) 2

y = sec^(-1)((1)/(2x^(2) -1 )), 0 lt x lt (1)/(sqrt(2))

y = sin ^(-1)(2xsqrt(1 - x^(2))),-(1)/sqrt(2) lt x lt (1)/sqrt(2)

If 1 lt x lt2 then what is the value of sqrt(x+2sqrt(x-1))+sqrt(x-2sqrt(x-1)) ?

If a=z_1+z_2+z_3, b=z_1+omega z_2+omega^2z_3,c=z_1+omega^2z_2+omegaz_3(1,omega, omega^2 are cube roots of unity), then the value of z_2 in terms of a,b, and c is (A) (aomega^2+bomega+c)/3 (B) (aomega^2+bomega^2+c)/3 (C) (a+b+c)/3 (D) (a+bomega^2+comega)/3