Question

- (1001). 110UICN11, 12. (2) Assume f(3) = Sad (0) 307w+1dw. Calculate f'(1 + i). (Show your work.)

Show all steps and label them please

This is a complex Analysis problem, so please solve it based on that.

Answer 1

WORKING - white cauchy integral formula a show that mati lies inside given dish. With the hell of cauchy integral formula, write f) in terme q3. find t') at and but Balti DETAILED SOLUTION

Cauchy integral foromale states that T F(W) que =at i F(3) I-11) w- where flue) is analytie inside and one while waa is a pont inside c. Herre c is AD310) per dish with centure at snigin and Kodi 2. clearly walti lies inside DD₂(0), Also, flue) =BW²7WH is analytic everywhere being a polynomial. Thus, from (1) ( 3u2t7wh = z21B2²+73+1) aby pod W-2 is waB eies in DD310) (Butuh - w-3 f(3) = 2*1372+72+) 2D₃10) Above relation is valid for all 3 sai eving insite DD31) f(3) = 2x1 (62+7) of'Q+1) = zri (((1+i) +7] > f'(+i) -211 (13761) 13' (ti) = 2671 -12* to L OC.