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# 5th roots of unity help watch

1. Hi, I need to put all the 5th roots of unity into the form of x+iy, but I've totally forgot how, also could someone describe to me in simple words a little bit what exactly roots of unity are, I know that there's 4 fifth roots of unity though
2. MEI FP2?

Can you multiply complex numbers using modulus-argument form OK? Visualise a unit circle, centre 0 on the Argand diagram. Now visualise starting at 1 and moving anticlockwise through one-fifth of a rotation (2pi/5). Do that five times and you're back to where you started. So the first move was a fifth-root of 1. There are four other numbers that share this property. Plot them all on the Argand diagram and admire the pattern.

If you're still on FP1, observe that you're trying to solve x^5-1 = 0. Spot one root easily, and divide out the factor you get using the factor theorem. Get a pretty quartic. You know that you are looking for roots in conjugate pairs, so the quartic will split into two quadratics. A bit messy.
3. Thank you, after I did hours of research last night, my head finally got round it all

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Updated: January 16, 2010
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