SOLUTION: I am looking for a general solution to a complex number raised to a complex power. I recall that Euler had a solution, but I can't recall what it was. However, it was in the form o

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I am looking for a general solution to a complex number raised to a complex power. I recall that Euler had a solution, but I can't recall what it was. However, it was in the form o      Log On


   



Question 300834: I am looking for a general solution to a complex number raised to a complex power. I recall that Euler had a solution, but I can't recall what it was. However, it was in the form of (something here) + i (something here), and used logarithms heavily (as is an Euler trademark). Any help will be greatly appreciated. Thanks.
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


To calculate :

Let taking the sign appropriately so that

Let

Then


John


Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
Euler's equation is:
e%5E%28theta%2Ai%29=+cos%28theta%29+%2B+i%2Asin%28theta%29
So