Page 94 - Calculus with Complex Numbers

(i) Put t = z - 2. Then z = t + 2. Therefore,

The range of validity of the geometric series is I //21 < 1. Therefore the

range of validity of the Taylor series is Iz - 21 < 2.

Range of validity is all t, therefore all z.

t 2 (3
Y
@
log z = logt/ + 1) = t - + - . . .

1 1 1 1 1
1 (t + 1)2 - 1 tl + lt lt 1 + tl l
c2 -

Simple pole with residue 1/2.