Hey All,

How would you find the following complex number problem:

find the four roots of the equation z^4= j3, expressing yuor answer in the form re^{jθ}, where r and θ are real. sketch their positions in an Argand diagram.

Thanks

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- May 1st 2007, 10:19 AMdadoncomplex no.
Hey All,

How would you find the following complex number problem:

find the four roots of the equation z^4= j3, expressing yuor answer in the form re^{jθ}, where r and θ are real. sketch their positions in an Argand diagram.

Thanks - May 1st 2007, 10:21 AMThePerfectHacker
- May 1st 2007, 10:25 AMdadon
well the question i copied it from is j3. unless their was a typo?

buy don't complex numbers have the form a +jb - May 1st 2007, 11:25 AMtopsquark
- May 1st 2007, 12:03 PMdadon
yes this is from an engineering book where j^2= -1

How about this question instead?

find the four roots of the equation z^4= -16, expressing your answer in the form a+jb, where a and b are real. sketch their positions in an Argand diagram. - May 1st 2007, 02:10 PMCaptainBlack
First you need to know or be able to derive:

j = e^{pi j/2 + 2 pi j n}, n=0, +/-1, ...

this is because: e^{pi j/2} = cos(pi/2) + j sin(pi/2) = j.

Now z^4 = j^3 = e^{3 pi j/2 + 6 pi j n}, and so:

z = e^{[3 pi j/2 + 6 pi j n]/4} = e^{3 pi j/8 + 3/2 pi j n},

Putting n =0, 1, 2, 3 should give four distinct values for z, and any

other value will again give one of these.

RonL - May 2nd 2007, 04:26 AMdadon