# Toronto Math Forum

## MAT334--2020F => MAT334--Tests and Quizzes => Test 1 => Topic started by: Maria-Clara Eberlein on October 14, 2020, 01:03:24 PM

Title: 2020 Night Sitting #1
Post by: Maria-Clara Eberlein 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?
Title: Re: 2020 Night Sitting #1
Post by: Milan Miladinovic 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 $n\in\mathbb{Z}$.
Title: Re: 2020 Night Sitting #1
Post by: Maria-Clara Eberlein on October 14, 2020, 03:54:06 PM
Okay makes sense, thank you!
Title: Re: 2020 Night Sitting #1
Post by: Xuefeng Fan 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)