Using permute function for rearrange or for transpose complex multi-dim arrays. Do I need to conj before?

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Hello
Please help me to understand: I figured out that for doing transpose of a complex multi-dim array (3d or 4d ...) I need to conjugate my array before, like:
permute(conj(A),[2 1 3]);
Am I right?
But then if I need only to rearrange the dimensions of my complex array (like 4th dimension will be 3rd) ,
Bnew = permute((B),[1 2 4 3]);
do I need to conjugate my array also?
I get confused, because later if do:
permute((Bnew),[1 2 4 3]);
I will get the same array as B, right?
Thank you!

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