Prove that 1+i is a root of the equation z^4+3z^2-6z+10=0. Find all the other roots.

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- Jul 31st 2006, 01:23 AMkingkaisai2Complex numbers-proving and finding roots
Prove that 1+i is a root of the equation z^4+3z^2-6z+10=0. Find all the other roots.

- Jul 31st 2006, 04:25 AMtopsquarkQuote:

Originally Posted by**kingkaisai2**

(Check.)

Now, if 1+i is a root, so is 1-i. Thus we know that

is a factor of . So do the division. This gives you a quadratic in z to solve, which you can do by factoring or the quadratic formula or whatnot.

-Dan