Geometric Sum, involving complex numbers
I came across an exercise involving both geometric sum and complex numbers.
I've read through Wikipedia and found: The summation formula for geometric series remains valid even when the common ratio is a complex number.
So, for the question:
A sequence has ten terms with first term , for . Each subsequent term is 2i times its previous term. That is, the 2nd term is .
The sum of this sequence is a + bi . What is the value of |a + b|?
If we wish to get the sum of the geometric progression we use:
Using this you only give headaches, since we are searching for a+bi solution.
So, what would be the best approach? --besides from calculating all the terms up to n=10.
Is it really possible to use the geometric sum formula here?