how to write code that performs the function

and how Evaluate the function at input values of x & n determined by the user, then keep the real part of the complex result at A and the imaginary part at B.

[KSSV]

What have you tried?

[abod farawi]

I am learning new and do not understand it well

[Torsten]

f = @(x,n) x.^(1i.^(n-1)+2./n) - 1i*abs(5*cos(exp(1i.*sqrt(n).*x)))
real(f(4,3))
imag(f(4,3))

[Walter Roberson]

Note: syms requires the Symbolic Toolbox be installed and licensed.

[Hiro Yoshino]

@Walter Roberson is right.

if you run it with Symbolic Math Toolbox, it goes as follows:

syms x n i

f = x^(i^(n-1)+2/n) - abs(5*cos(exp(1i*sqrt(n)*x)))

f = 

[Walter Roberson]

I think i = sqrt(-1) there, and also a trailing i got missed

syms x n 
f = x^(i^(n-1)+2/n) - abs(5*cos(exp(1i*sqrt(n)*x)))*i

[Torsten]

@abod farawi

Since you don't seem to have a licence for the symbolic toolbox, I showed you a way how to circumvent symbolic computations.

And since you don't want to "solve" or "dsolve" anything, I also don't see the necessity to go the symbolic way.