I need to find the fourth root of -81. Thank you in advance.

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- Jun 8th 2009, 10:18 AMNevershNth root of a complex number:
I need to find the fourth root of -81. Thank you in advance.

- Jun 8th 2009, 10:28 AMMoo
- Jun 8th 2009, 10:33 AMHallsofIvy
[QUOTE=Moo;327307]Hello,

-81=(-1)*(81)

The 4th root of 81 is 3 (because 81=9x9=3x3x3x3)

Now, what is the 4th root of -1 ? Write , where k is an integer

And then take the fourth root of

Typo: This should be either or

Quote:

: (k=0,1,2,3) then as k grows up, you'll get back to these solutions...

- Jun 8th 2009, 10:38 AMpankaj
Let x be the fourth root of -81.

By**De-Moivre's theorem**

;k=0,1,2,3