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complex numbers

Name: Anonymous 2007-10-31 19:26

Find the roots of the equation (z+1)^3 = 1, in the form x+iy.

gogogo

Name: Anonymous 2007-11-01 23:51

>>6
Isn't that a little complex for this problem?

>>7
You did that on purpose, huh?  Sneaky.

>>8
I dunno what you're talking about, but I like it.

Since the assignment is probably past due, I wanna try.

Normally you would just find the roots of the terms inside the brackets, but the 1 complicates things.  it must first be subtracted.  You then do the trinomial expansion of the factored polynomial.  You can find the terms by using Pascals triangle and the form  a^n*b^0 + a^n-1*b^1 + ... + a^0*b^n.  (or just use the trinomial expansion theorem). 

Next you need to combine your terms.  The -1 will cancel at this point.  You should be able to factor, as 7 did, making one of your roots 0, and giving you a quadratic equation to solve.  Once you've solved for your solutions, if there is a negative square root, factor that out as i, and you have your answer.

Good job 7.  You da man.

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