Toronto Math Forum
MAT3342020F => MAT334Tests and Quizzes => Test 1 => Topic started by: MariaClara 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?

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 $n\in\mathbb{Z}$.

Okay makes sense, thank you!

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)