Complex analysis proof (easy but cant figure out)?

Question

So I've been racking my brain over this and it seems like an extension of the triangle inequality. Anyways, here it is.

Prove that the length of the summation from k=1 to n of z_k is less than or equal to the summation from k=1 to n of the length of z_k.

Answer 1

Yes, that's what it is: an extension of the triangle inequality.

Use induction.