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 $6$.

Astudent must have an average on five test that is greater than it equal to 80% but less than 90% to receive a final grade of b. devon's greades on the first four test were 78% 62% 91% and 80% what range if grades on the fifth test would give him a b in the course? ( assuming the highest grade is 100%)