Question

Write all the right and left cosets of h={-1,1} in the multiplicative group g={1,-1,i-i}

Answer 1

Let H = {-1, 1} and group G = {1, -1, i, -i} under complex multiplication.

Right Cosets of H in G:

H(1) = H(-1) = H = {-1, 1},

H(i) = H(-i) = {-i, i}.

Left Cosets of H in G:

(1)H = (-1)H = H = {-1, 1},

(i)H = (-i)H = {-i, i}.