Solve for x - - - my challenge problem

[lookagain]

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Let x belong to the set of complex numbers.


Find at least two solutions for x (or two solutions if there are no more than two solutions) for the following equation:


\(\displaystyle x^{(x - 4 - i)} \ = \ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)[The exponent is (x - 4 - i).]

 

[daon2]

.
.

Let x belong to the set of complex numbers.


Find at least two solutions for x (or two solutions if there are no more than two solutions) for the following equation:


\(\displaystyle x^{(x - 4 - i)} \ = \ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)[The exponent is (x - 4 - i).]

By inspection I see \(\displaystyle x=1, i, 4+i\). I do wonder if the complex log can be used for more solutions, I attempted it but was not satisfied by the mess I made with my symbol soup