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Question

Can I be an exponent for any variable


Solution

Your question is very vague.

If you are talking about the number 1,

Any number or variable raised to 1 is the number or the variable itself.


x^1 = 1


If you are talking about the complex number i =√(-1) , then the answer is yes but to understand more about that stuff, you need a lot more knowledge in trigonometry and logarithms.


I will provide the solution below.
 

Consider a real number A, and take it to the power i. If our system of complex numbers is to be consistent, then A^i must be a complex number; in other words, there must be two real numbers x and y, which depend on A, such that:

A^i=x+iy


Soln :

A^i = e^(i*lnA)

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