Final Answer
Step-by-step Solution
Problem to solve:
To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=-1$ and $c=1$. Then substitute the values of the coefficients of the equation in the quadratic formula:
- $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)
Calculate the power $\sqrt{-3}$ using complex numbers
Calculate the power $\sqrt{-3}$ using complex numbers
Split the fraction $\frac{1+\frac{3}{\sqrt{3}}i}{2}$ in two fractions with common denominator $2$
Split the fraction $\frac{1-\frac{3}{\sqrt{3}}i}{2}$ in two fractions with common denominator $2$