What is 1i^1i = 0.208 ?

[lvl107]

Hello, Everyone.

Thanks in advance for your time and help.

Best Regards.

[Werner_E]

What exactly is the question?

0.208 is one out of an infinte number of results for i^i. The exact value is exp(-pi/2).

Or is the question about the mathematical derivation of that result?

[lvl107]

Oh, many thanks, Werner. I got it. . And :

Thanks in advance again.

Best Regards.

[StuartBruff · Accepted solution]

Simply express i in polar form, then raise it to the power of i (ie, multiply the exponent by i) then evaluate.

Stuart

[lvl107]

Many thanks, Stuart. I'm really a new with "polar". I'll check it out. And I got it. . And now I have to go to work.

Thanks again.

Loi.

[Werner_E]

Or here a derivation considering the ambiguity of that expression.

BTW, i^i = exp(-pi/2) simply isn't true. The RHS is a single scalar while the LHS represents an infinite variety of values - that cannot be equal and the symbolic processor seems to be aware of that.

Mathcad sure is a good tool for applying maths, but not necessarily for learning maths. A good book about the subject you are iterested in is the better choice IMHO.