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Complex bessel function


I am currently trying to isolate the real and imaginary components of
first and second order modified Bessel functions.  For example, I have a
function expressed as



F=BesselI[0,sqrt(i)*a+b], where i is the imaginary unit.  Both a and b
are positive real.  I need to separate out the real and imaginary
components of F symbolically.  I have tried Re, Im, ComplexExpand, I
have used Assuming to define a and b as real and 0<a<infinity and
0<b<infinity.  I have tried ComplexExpand.  I have tried Refine[Im[F]].
I loaded the package ReIm.



All of these functions do a fine job separating the real and imaginary
components when I provide numeric values for a and b, but are unable to
solve symbolically.  I thought Refine was supposed to solve symbolically
as if a numeric value has been assigned to the variables (with the value
range of the variable defined by Assuming or the assumptions listed in
Refine)?  Am I missing some simple trick to solve this symbolically, or
is this not possible?



Thanks in advance!

Zach 




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