blaque678
  • blaque678
Find all solutions, real and complex of the equation x^3=1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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tkhunny
  • tkhunny
This is not all that tricky once you have seen it. Such complex roots are spaced evenly around the origin. Since we seek three, we'll need \(\pi/3\) or 120ยบ between each one. Since also there is a trivial solution, x = 1, the other two are not hard to find.
anonymous
  • anonymous
\[\frac{2\pi}{3} \]
Luigi0210
  • Luigi0210
I hope you're not giving an answer pg

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anonymous
  • anonymous
uh... no just fixing a boo boo
Luigi0210
  • Luigi0210
Just making sure :P
tkhunny
  • tkhunny
Let's see, \(\2\pi / 3 = \dfrac{2\pi}{3}\). What do you know! Sorry about that. Boo boo acknowledged and repaired.
tkhunny
  • tkhunny
Okay, my typing just keeps getting worse. Might be time for a break.
anonymous
  • anonymous
no worries!
blaque678
  • blaque678
I don't know how to the problem at all
tkhunny
  • tkhunny
There are at least two ways to do this one. One pretty fancy. I was trying to hint at it, above. We also have algebra. To find the solutions to x^3 = 1, we solve x^3 - 1 = 0. Are we feeling better about that "at all" thing? It is hoped that you have factored and solved such equations, before.
blaque678
  • blaque678
ok so x=1 and the other two are a quadratic equations?
tkhunny
  • tkhunny
Yes, you can use the quadratic formula to find the other two. You can think to the future at the exciting other ways there are to find such solutions. Good work. I invite you to plot these three solutions and ponder on the first answer. See how they are evenly spaced around a circle?

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