### Author Topic: 2020 Night Sitting #1  (Read 900 times)

#### Maria-Clara Eberlein

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##### 2020 Night Sitting #1
« on: October 14, 2020, 01:03:24 PM »
When I solve the equation w^2+w+1=0, I got two complex roots instead of two real roots. Is there an i missing from the value of w?

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##### Re: 2020 Night Sitting #1
« Reply #1 on: October 14, 2020, 02:52:16 PM »
I got 2 complex roots as well. It looks like there's a slight typo, should be $e^z = \dfrac{-1 \pm i\sqrt{3}}{2}$, so we get the same answer as the solution: $log\left(\dfrac{-1 \pm i\sqrt{3}}{2}\right) = \left(\pm\dfrac{2}{3} + 2n\right)i\pi,$ for $n\in\mathbb{Z}$.

#### Maria-Clara Eberlein

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##### Re: 2020 Night Sitting #1
« Reply #2 on: October 14, 2020, 03:54:06 PM »
Okay makes sense, thank you!

#### Xuefeng Fan

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##### Re: 2020 Night Sitting #1
« Reply #3 on: December 07, 2020, 02:28:14 PM »
After finding out that e^z=-\frac{1}{2}\:i\frac{\sqrt{3}}{2}
We can take ln and get the answer that z =i(+- (2/3)pi +2kpi)