Question

Find the disk of convergence of power series IM: (= –2+i)" 2" where, z = x + iy n=0

Answer 1

(2-2 + )" ; where f/2) = Power Series - 2 zxriy nzo دوو (2-(2-2))" an nro 00 an nzo General form of buser dories - 8/2) = E , (2-20) where Zo is complex constand, centre of disk of an nth complex caufficient Convergence 2 → Complex variable formula for Radius of Coronzena (ROC) (R) lim sup jan 13 = R Hore and an Zo = = 2- Ana R = 2 ling! 2 R nto an Now disk of convergence on either Iz-Zo]<2 ar /2-2012 We have to check boundary of the disk . Boundary Rod of disk is /2-(2-2)) = 2 can put that a complex number Z-20)=2 d We

we know whas modulus value is 2. {:: 12.- (2-1) ) = 2] I el = 1 ; Put z- (2-1) = 2 eo in in f(2) Imagine the point graphically - 20 = (2, -1) {: 2+x+18] So; 8/2) = 8 (2018) 1 gen hao pino nzo 2 unit (2,-1). Mo o disk nzo which is Not Convergent So, we must enclude boundary [Just for Imagination ] Equation of urcle is 12-20)=12elo Hence disk of Convergence 12-(2-2)<d in disk of convergence. is disk of ie consegme. ( Excluding bunday) He