SOLUTION: Find the general value of -i to the power -i

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Question 1039219: Find the general value of -i to the power -i
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

%28-i%29%5E%28-i%29

We use Euler's equation 

e%5E%28i%2Atheta%29=cos%28theta%29%2Bi%2Asin%28theta%29

Substitute theta=-pi%2F2



matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0Ae%5E%28i%2Aexpr%28-pi%2F2%29%29%29=-i

Raise both sides to the -i power







matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0Ae%5E%28-pi%2F2%29=%28-i%29%5E%28-i%29%29

Edwin