Question

Find the following: z2+9 e) lim 23į 2-3i z2+i f) lim 2-i 24-1 Write given numbers in the polar form reio: 3 a) (cos 29 + i sin 27)

Answer 1

L' Hospital Reele : If we have indeterminate form (0/0) or 100%), then we have to dillexen Hiete both Numerator and denominator and then but the limit value. & es Lim 2°+9 (31)2 + 9 3i-3i 23i 2-si and then only 102 = -1 Lim z²+9 -9+9 - % 2 i 2-zi 3i-3i which ej indelerminate form, so dost went we have delleenhate Denominator and Numerator wirid 2 and then kut 2= 3 (227 *+9) Lam 22 to Dillesen hahen of 23 dz Lim (22) dx 3i So Lim de la Condant =0 2*31 (2-31) 23i 1-0 = 2-3 Gil Ans Im 229 23i Z-31 -yti 1-1 1 -lti :-17 z = Lim 5 ) (0)? 27 i 24_ 101-1 Anay thung divided by o ij infnile , 10, .d 2"t1 Am - 2-) i ( 24_1 Note: 1) We can not use L'Hospital Rele as (-1+0/0, is not in determinate for i) 1 : Complex Number 1) X = -1 os Scanned with 4 - 1 1 CamScanne

3 (CN + 9 eio = (3 Lel o = 21 o iaalg a Giren Giren [ Cos de i sin off We also know that euler's Identity Cos o + i sino [Con este ti sin(*)] - inlo exprenion @ Pulting value of equchon 3 i 27 x3 [ (in e tyre sin (957- Le canla] = e :-/ [cos (en Jei sin (87)] 9 الح e 3 27 5 I And ro where s=1 : 0= 22/3. axb e ab. (eajo CS Nolened' with Scanner e