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Best answer by StuartBruff

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

Stuart

3 replies

W
Werner_E25-Diamond I
25-Diamond I
March 7, 2014

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?

L
lvl10720-TurquoiseAuthor
20-Turquoise
March 7, 2014

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

What+is+1i%5E1i+%3D+0.208+%282%29+.PNG

Thanks in advance again.

Best Regards.

S
StuartBruff23-Emerald VAnswer
23-Emerald V
March 7, 2014

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

Stuart

L
lvl10720-TurquoiseAuthor
20-Turquoise
March 7, 2014

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.

W
Werner_E25-Diamond I
25-Diamond I
March 7, 2014

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.

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