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Complex Analysis
Let f(z) = [ Sin ^2 z . (1+cosz) ] / [ {(z-1)^2}-1 ]
1- find the zeros of f
2- classify the zero z=0 , z= pi, z=2pi
1- find the zeros of f
2- classify the zero z=0 , z= pi, z=2pi
Complex Analysis
f(z) = sin ( 1/(z-pi)) / 2z
1- Find the singularities of f , and all possible annulus centered at each singularity
2- Find the laurent series of f in each annulus
3- classify each singularity
4- compute the residue of at each singular point
1- Find the singularities of f , and all possible annulus centered at each singularity
2- Find the laurent series of f in each annulus
3- classify each singularity
4- compute the residue of at each singular point
Complex Analysis
use the maclaurin series of f(z)= [ (cos ^2) of z] - [ (sin ^2) of z ]
to compute integral on Curve for ( [ (cos ^2) of z] - [ (sin ^2) of z ] ) / ( z^53)
C :|z|=2 oriented positively
to compute integral on Curve for ( [ (cos ^2) of z] - [ (sin ^2) of z ] ) / ( z^53)
C :|z|=2 oriented positively
Complex Analysis
find radius and disk of convergence
1) series from 1 to infinity of [ (z+5i)^ ] / [ n ^ square root of n ]
2) series from 3 to infinity of [z^n ] / [ n(n+i)(n+2)
1) series from 1 to infinity of [ (z+5i)^ ] / [ n ^ square root of n ]
2) series from 3 to infinity of [z^n ] / [ n(n+i)(n+2)
Complex Analysis
Find Sum of power series ,then answer the questions
1- series from 1 to infinity of [ {(-1)^(n+1)} .{ n} . { (z-1)^n} ] indicate the convergence nhd (neighborhood).
is series from 1 to infinity of [ n. {(1-4i)^n} convergent if yes compute its sum
1- series from 1 to infinity of [ {(-1)^(n+1)} .{ n} . { (z-1)^n} ] indicate the convergence nhd (neighborhood).
is series from 1 to infinity of [ n. {(1-4i)^n} convergent if yes compute its sum
Complex Analysis
Find Sum of power series ,then answer the questions
series from 2 to infinity of [ 3 ^(n+1) . {z^n+2)} ] indicate the convergence nhd (neighborhood).
is series from 2 to infinity of [ 3 ^ {(3n+4)/2} /n!) convergent if yes compute its sum
series from 2 to infinity of [ 3 ^(n+1) . {z^n+2)} ] indicate the convergence nhd (neighborhood).
is series from 2 to infinity of [ 3 ^ {(3n+4)/2} /n!) convergent if yes compute its sum
Complex Analysis
Use Maclauin series of
E^z to compute
series from 0 to infinity of
[Cos (n.phi/3) ] / [ n!]
E^z to compute
series from 0 to infinity of
[Cos (n.phi/3) ] / [ n!]
Complex Analysis
Find Taylor series of the function :
f(z) = 4 (z^3)+ 2 (z^2)-z-5 center Zo = -1
f(z) = cube-root of [ Exp ^(z-2)] center Zo=i
f(z)=e^z . Cosh z center Zo=0
f(z) = 4 (z^3)+ 2 (z^2)-z-5 center Zo = -1
f(z) = cube-root of [ Exp ^(z-2)] center Zo=i
f(z)=e^z . Cosh z center Zo=0
Complex Analysis
Find if these sequence convergent of divergent ( details )
1) Zn = [ i.(z^n) - n.(3^(n+1)) ] / [ i.n .(2^(n-1)) ]
2) [ conjugate ( 4 n^2- i n +1 ) ] / [ (i n +3) ^2 ]
3) [ 8 ^ (n+1) - 5^(n) ] / [ 5 . (8^n)+ 3 ^(n+1)]
1) Zn = [ i.(z^n) - n.(3^(n+1)) ] / [ i.n .(2^(n-1)) ]
2) [ conjugate ( 4 n^2- i n +1 ) ] / [ (i n +3) ^2 ]
3) [ 8 ^ (n+1) - 5^(n) ] / [ 5 . (8^n)+ 3 ^(n+1)]
Complex Analysis
Find if these sequence convergent of divergent ( details )
1) [ (1+i)^(1/n) ] / square root(n-1)
2) [2^n! ] / [2^ (n+1)! ]
3) sin ((1+i)/n)
1) [ (1+i)^(1/n) ] / square root(n-1)
2) [2^n! ] / [2^ (n+1)! ]
3) sin ((1+i)/n)
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