Show that the real part of any solution of $\displaystyle (z + 100)^{100} = (z - 1)^{100}$ must be 0.

Now in the book they solve it by starting: $\displaystyle (z + 100)^{100} = (z - 1)^{100} \Rightarrow (z +1) = (z - 1)e^{\frac{2\pi ki}{100}}$.

I understand the steps that follow it, however I don't understand that step. I referred to the definition of m-th roots of complex numbers, which says: $\displaystyle z^{1/m} = |z|^{1/m}e^{i(\theta + 2k\pi)/m}$

What am I missing? Thanks in advance.