Write the following in set-builder form :- 1. C = {1, -1, i, -i} Write the following in roster form :- 1. D = {x : x = cube roots of unity}. Share with your friends Share 7 Vijay Kumar Gupta answered this 1.Consider the following set C=1, -1, i, -iFind the quation whose roots are 1, -1, i, -iThe equation is given by, x-1x+1x-ix+i=x2-12 x2-i2 =x2-1x2--1 since i2=-1 =x2-1x2+1 =x22-12 =x4-1Therefore the required set bulider form is given by, C=x : x∈R, x4-1=0 Consider the following set. D=x: x=cube root of unityFind the cube root of unity. x=113This can be rewritten as, x3-1=0Factorize the LHS to get, x-1x2+x+1=0 Equate first factor to zero to get, x-1=0⇒x=1Equate second factor to zero to get, x2+x+1=0Use quadratic formula to find the roots x=-1±12-41121 =-1±1-42 =-1±-32 =-1±i32 Thus the three roots are 1, -1+i32, -1-i32So the required roster form of set is D=1, -1+i32, -1-i32 6 View Full Answer
