Question: Cannot find all of roots of complex variables function

Hello everybody,

I want to find all of roots of the complex variables functions in two ways.

(1) find the value which can make the function equals 0

(2) find the real value and imaginary value which make real part and imaginary part of function equal 0

(I know answers of these two case is not equal completely.)


The function is a non-linear function, including sin, cos and Bessel function, such as:


And, I used Analytic and fsolve to do case (1) and (2), but failure. The follow result is how I tried to find the real value answer:


It seems that both of two commands can only find some of roots. 

How to find all of roots of these cases? The related .mw file is attached.


Thanks a lot.


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