Find the number of positive integers n that satisfy 2^{200} < n^{1000} < (130n)^{5000}.
For this problem, you must consider magnitude of complex numbers geometrically.
For the first part, the answers are |v| = 2, |w| = 3, |z| = 3.
For the second part, the answers are |v + w| = sqrt(2), |w + z| = 2, |z + v| = sqrt(3).
+2653 
