Hello friends,

cant find the root here!

: Find the sixth roots of (12+5i)

Thanks,

Harshal

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- Apr 4th 2007, 02:43 AMharshal54321complex number
Hello friends,

cant find the root here!

: Find the sixth roots of (12+5i)

Thanks,

Harshal - Apr 4th 2007, 05:24 AMCaptainBlack
convert the number to polar form:

12 + 5i = 13 e^(i [arctan(5/12) + 2 pi N]), N=0, +/-1. +/-2, ..

then the sixth roots are:

(12 + 5i)^(1/6) = (13)^(1/6) e^(i [arctan(5/12) + 2 pi N]/6), N=0, +/-1. +/- 2, ..

Which give distinct values for N= 0, 1, 2, 3, 4, 5.

RonL - Apr 4th 2007, 06:25 AMSoroban
Hello, Harshal!

I assume you're familiar with DeMoivre's Theorem . . .

Quote:

Find the sixth roots of (12 + 5i)

Convert to polar form: .12 + 5i .= .13(cosθ + i·sinθ), .where θ = arctan(5/12) .*****

Then: .(12 + 5y)^(1/6) . = . 13^(1/6) (cos[θ + 2kπ)/6] + i·sin[(θ + 2kπ)/6])

. . Evaluate for k = 0, 1, 2, 3, 4, 5

*****

Edit: corrected my typo.

. . . .Thanks for pointing it out, Captain. - Apr 4th 2007, 08:15 AMCaptainBlack