Recent content by mariab89

Yes, sorry my question is to determine whether there exists a power series that converges at z = 2 + 3i and diverges at z = 3 - i.

Homework Statement does there exist a power series that converges at z= 2+31 and diverges at z=3-i Im really stuck on this one! any ideas?

Well.. I was thinking maybe the group of reflections. But then that wouldn't form a group since (reflection * reflection = rotation) any hints?

ohh ok so then D6 has 4 distinct cyclic subgroups... (I) - generator is the identity (R1)=(R5)= {I, R1, R2, R3, R4, R5} - generator is R1 or R5 (R2)= (R4) = {I, R2, R4} - generator is R2 or R4 (R3) = {I, R3} I'm just wondering what about the reflections? would they be cyclic...

So, then would I itself be a subgroup? also, {I, R1, R2, R3, R4, R5} and {I, S1, S2, S3, S4, S5, S6}?

Homework Statement Recall that given a group G, we defined A(G) to be the set of all isomorphisms from G to itself; you proved that A(G) is a group under composition. (a) Prove that A(Zn) is isomorphic to Zn/{0} (b) Prove that A(Z) is isomorphic to Z2 Homework Equations The Attempt at a Solution

Homework Statement (a) How many distinct cyclic subgroups of D6 are there? Write them all down explicitly. (Here, D6 is the dihedral group of order 12, i.e. it is the group of symmetries of the regular hexagon.) (b) Exhibit a proper subgroup of D6 which is not cyclic. Homework...

oh ok i see now! Thanks a lot!

so to show that what i did was... exp(Log(-z) + i*pi) = exp(Log(-z))exp(i*pi) = (-z) (-1) = z but.. I am still unclear how this shows that Log(-z) + i*pi is a branch of log z.

Homework Statement Show that the function Log(-z) + i(pi) is a branch of logz analytic in the domain D* consisting of all points in the plane except those on the nonnegative real axis. Homework Equations The Attempt at a Solution I know that log z: = Log |z| + iArgz + i2k(pi)...

Homework Statement Prove that for any isomorphism \phi : G--> H |\phi(x)| = |x| for all x in G. is the result true if \phi is only assumed to be a homomorphism? Using the solution to the above proof or otherwise, show that any 2 isomorphic groups have the same number of elements of order n...