Use polar exponential form for complex numbers in this probl

Use polar/ exponential form for complex numbers in this problem (re^i(theta) form).

(a) write out the binary opration tables for Z6= <Z6+6> and U6= <U6, . >. Order the rows and columns in a sensible way.

(b) Prove that the map f: Z6 approaches U6 given by k maps to (e(2pi/6)i)^k is an isomporphism of binary structures.

(c) Find a different isomporhism of binary structures, g:Z6 approaches U6, and prove your answer is an isomorphism.

Solution

what is <Z6+6> and U6