Introduction to Fourier analysis 1The Genesis of Fourier analyses

3Exercises

1
(a) distance from point to Origin on complex plane
(b) x!=0 or y!=0 |z|≠0 |z| \neq 0, so x=0 and y=0
(c) The calculation can be carried in
(d) The preceding equals sign is calculated, and the following inequalities are squared and persisted.
(e) Take-in calculations

2
(a) x axisymmetric
(b) Carry-in calculations
(c) Z=cosα+isinαz=\cos \alpha+i\sin \alpha z¯=cosα−isinα\overline z=\cos \alpha-i\sin \alpha

3
(a) There are 2 limit w1w2 w_1 w_2, then w1−w2=w1−wn− (w2−wn) w_1-w_2=w_1-w_n-(w_2-w_n) n approaching Infinity is equal to the right of 0, so w1=w2 w_1=w_2
(b) It's easier, the opposite is a little more troublesome todo
(c) Due to an a_n part and convergence, so, for any ϵ\epsilon, there is N, when n>m>n,∑nmai<ϵ\sum_m^na_i, due to |zi|<ai |z_i|