This integral, after calculation, contains the root of a complex number.
$$\int_{-7}^{3+2i}{\frac{dz}{(1-z)^{\frac{2}{3}}}} = 6-3\cdot(2-2i)^{\frac{1}{3}}$$
What should I do to get one number in the answer, not many. In the problem statement it is said to consider $\sqrt[3]{8} = 2\space$. The Wolfram Mathematica package, when calculating this integral in the answer, gives one number. Wolfram solve
Define a branch cut along the positive real axis, therefore, the argument of a complex number $z$ is $\theta \in (0, 2 \pi)$. With this choice, we have the function inside integral sign holomorphic for all values of $z$ except for the points on the branch cut. By the fundamental theorem of Calculus for complex function: $$\int_{-7}^{3+2i}{\frac{dz}{(1-z)^{\frac{2}{3}}}} = \frac{1}{3} (1-z)^{\frac{1}{3}} \Big|_{-7}^{3+2i} = 6-3\cdot(2-2i)^{\frac{1}{3}}$$