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Complex numbers help

by kay
Tags: complex, numbers
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kay
#1
Jul6-14, 08:02 AM
P: 21
We know that i^3 is -i .
But I am getting confused, because I thought that i can be written as √(-1) and i^3 = √(-1) √(-1) √(-1) = √(-1 -1 -1) = √( (-1)^2 -1) = √(1 -1) = √(-1) = i
( and not -i ).
Please help.
Sorry I couldn't use superscript because I was using my phone.
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micromass
#2
Jul6-14, 09:01 AM
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P: 18,240
http://www.physicsforums.com/showthread.php?t=637214
dieterk
#3
Jul6-14, 10:22 AM
P: 1
i definitely is not \sqrt{-1}. If you like (abuse of notation)
\sqrt{-1} = \pm i
Using (this not correct notation) \sqrt{-1}^3 = \pm i. Much better is of course
i^3 = (i*i)*i = -1*i = -i

kay
#4
Jul6-14, 10:38 AM
P: 21
Complex numbers help

i am really not familiar with Euler's constant that much, and complex calculus, but thanks. :)
kay
#5
Jul6-14, 10:39 AM
P: 21
Quote Quote by dieterk View Post
i definitely is not \sqrt{-1}. If you like (abuse of notation)
\sqrt{-1} = \pm i
Using (this not correct notation) \sqrt{-1}^3 = \pm i. Much better is of course
i^3 = (i*i)*i = -1*i = -i
I didn't understand anything. :|
electronicsguy
#6
Jul7-14, 09:25 AM
P: 7
Quote Quote by kay View Post
i am really not familiar with Euler's constant that much, and complex calculus, but thanks. :)

The link given by micromass has everything you need to know and you don't need to know Euler's Formula to understand what he meant. I suggest read (not skim) the link provided by micromass.
HakimPhilo
#7
Jul9-14, 03:59 PM
HakimPhilo's Avatar
P: 65
When you got to this point: $$\sqrt{-1}\cdot\sqrt{-1}\cdot\sqrt{-1}=\sqrt{(-1)\cdot(-1)\cdot(-1)},$$ you made a mistake since [itex]\sqrt{a}\sqrt{b}=\sqrt{ab}[/itex] isn't true when [itex]a,b\lt0[/itex].


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