- #1

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*n*th power only work if

*n*is an integer value?

E.g. if I try to raise (2-2i) to the power of 3.01 then my manual calculation get a different result than my calculator, but for all integer values it works.

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- Thread starter jkristia
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- #1

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E.g. if I try to raise (2-2i) to the power of 3.01 then my manual calculation get a different result than my calculator, but for all integer values it works.

- #2

cepheid

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nth power only work ifnis an integer value?

E.g. if I try to raise (2-2i) to the power of 3.01 then my manual calculation get a different result than my calculator, but for all integer values it works.

Well, at least according to the Wikipedia article on the subject, 'n' must be an integer:

http://en.wikipedia.org/wiki/De_Moivre's_formula

- #3

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argh, I missed that. Thanks

Do you know how I can raise a complex number by a real number?

- #4

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I may be wrong but in mathematics, *n* is used to denote an integer by convention.

- #5

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I think you are right.

- #6

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Do you know how I can raise a complex number by a real number?

You can raise it to any power by using this method:

[itex]z^w = e^{ln|z^w|} = e ^{w \cdot ln|z|}[/itex] and simplify from there. From the top of my head, I believe this formula gives an infinite number of solutions depending on how you choose your branch of the logarithm.

- #7

HallsofIvy

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- #8

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http://www.suitcaseofdreams.net/De_Moivre_formula.htm

(cos+i sin)p/q = cos((p/q))+i sin((p/q)). (1.27)

So the decimal power should work as well, right?. I will try and convert the decimal to a fraction, but I dont see why it would make a difference.

When I tried it worked correct for quadrant I and II, but I could not get it right for III and IV.

I will keep playing with this.

- #9

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For quadrant II

θ=(atan(im(z)/re(z))

And for III

θ=(atan(im(z)/re(z))

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