For the complex equation , prove that the sum of the four solutions is always zero, no matter what size is.

This is what I've done so far.

Can someone please teach me how to do the rest? Thanks in advance (Headbang)

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- April 10th 2011, 04:00 AMwomatamaComplex Number Proof
For the complex equation , prove that the sum of the four solutions is always zero, no matter what size is.

This is what I've done so far.

Can someone please teach me how to do the rest? Thanks in advance (Headbang) - April 10th 2011, 04:11 AMProve It
Rewrite it as .

This means that the first fourth root is .

The other fourth roots are evenly spaced around a circle, so differ by an angle of . What are the other solutions? What do you get when you add them together? - April 10th 2011, 06:16 AMawkward
A little twist on ProveIt's approach:

Let , so the equation can be written

.

If the roots are , then we must have

.

If we expand the right-hand side of this equation, what can we say about the coefficient of ?