Let $z$ be a complex number, and let $n$ be a positive integer such that\[z^n = (z + 1)^n = 1.\]
a) prove that $|z| = |z+1| = 1$.
b) find the possible values of $z$ in exponential form.
c) prove that $n$ must be divisible by $6$.

2. (09.01 lc) a function is shown in the table. x g(x) −3 17 −1 −3 0 −4 2 13 which of the following is a true statement for this function? (5 points) the function is increasing from x = −3 to x = −1. the function is increasing from x = −1 to x = 0. the function is decreasing from x = 0 to x = 2. the function is decreasing from x = −3 to x = −1.