(1) For

ninZ

, let

\\\\gamma _(n):[0,1]->C,\\\\gamma _(n)(t)=cos(2\\\\pi nt)+isin(2\\\\pi nt)

.\ (a) Show that for all

m,ninZ,\\\\gamma _(m)

and

\\\\gamma _(n)

are homotopic in

C

.\ (b) For what

m

and

n

are

\\\\gamma _(m)

and

\\\\gamma _(n)

komotopic in

(C)/(/){0}

?

(1) For nZ, let n:[0,1]C,n(t)=cos(2nt)+isin(2nt). (a) Show that for all m,nZ,m and n are homotopic in C. (b) For what m and n are m and n Lomotopic in C\{0}