MAT334--2020F > Test 1

2020 Night Sitting #1


Maria-Clara Eberlein:
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?

Milan Miladinovic:
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:
Okay makes sense, thank you!

Xuefeng Fan:
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)


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