using the method of partial fractions obtain the expansion of
1-s/ s^2(s^2+1)
Im not sure how to go about it as you cant factorise the s^2+1
Im just going wrong everywehre
When i put i in i get
1-i = (Ci+D)(i)(-1)
1-i = (-c+Di)(-1)
1-i = C-Di
so i get C=1 and D = 1 which isnt right
aslo when i do A and B i end up with
1-s= As^4 + As^2 = Bs^3 +Bs + Cs^4 + Ds^3
equating terms in s gives me B=-1 and equating either s^4 or s^2 gives me A as 0
=
So:
Thus
A + C = 0
B + D = 0
A = -1
B = 1
So
C = 1
D = -1
Thus:
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In terms of the complex denominators:
=
So:
Thus:
A + C + D = 0
B - iC + iD = 0
A = -1
B = 1
So
C + D = 1
-iC + iD = -1
So
C = (1/2)(1-i)
D = (1/2)(1+i)
Thus:
-Dan