@dharr The answer is the same, whether we use manual substitution or evalc (as seen in the attached image). However, your approach is more appropriate: I should separate lambda1 into real and imaginary parts and then use evalc. 

@dharr When I take 'conjugate(q)', the 'bar' is on the entire expression. 

@dharr They are not complex of each other. They are different equations as you can see in the attached image (epsilon =1). 

@mmcdara x2, x1 in (3), and s2 in (5).

@mmcdara I need expressions as in the attached image. 

@sand15 Thanks. Is there any other wat to transform this set of PDEs into ODEs and solve it by RK scheme? I used the ansatz 'q=f(x-ct)', etc. Any other option?

@sand15 I did not delete it and I don't know who moved the last question. In 'Are_you_ok_with_that.mw' you found the determinant of B matrix (which is 8x8). But the following matrix is B11num1 (which is 9x9) as seen in this thread. Still, I could not find the determinant of B11num1. The system remains shows 'Evaluating' when I execute 'B11num2 := Determinant(B11num1)'

@sand15 For the 8x8 matrix, it works. But for 9x9 (as you can see 'B11num2' in https://www.mapleprimes.com/questions/237066-Determinant-The-System-Hangs), it doesn't work.

@sand15 I choose these parametric values 'para := {H__11 = 0, H__12 = 0, H__13 = 0, H__14 = 0.3, H__15 = 0, H__16 = 0, H__17 = 0, H__18 = 0, H__33 = 1.5, H__34 = 0, H__38 = 0.15, H__44 = 1.5, H__55 = 0, c__1 = 0.5, nu = 1, alpha__1 = 1.5, alpha__2 = 1, lambda__1 = 0.58*I, lambda__2 = 0.68*I, conjugate(lambda__1) = -0.58*I, conjugate(lambda__2) = -0.68*I}'. But with these values (where almost every entry of H takes zero except a few). But still, it's not evaluating. 

@sand15 Can we choose some suitable values of parameters (except x and t) that we get the determinant in https://www.mapleprimes.com/questions/237066-Determinant-The-System-Hangs? 

@sand15 I am just trying to solve the determinant https://www.mapleprimes.com/questions/237066-Determinant-The-System-Hangs and then plot it. No need to read the expression explicitly.

@acer @sand15    The status remains 'Evaluating' on the taskbar when I try to calculate the determinant of the 9x9 matrix. How to fix it?

Download determinant_edited.mw

@tomleslie {alpha,c,gamma} are constants. However, {w and k} are variables. We can assign a range of 'w'.

@nm On the page, it is mentioned that 'Before beginning the loop, assign i to a starting value'. As you can see in my code. I assigned the starting value of i.

@nm I changed elseif to elif. But this time I received 'Error, cannot determine if this expression is true or false:'