When is the Product \(P(k)=\prod_{n=1}^k(n+i)\) Purely Imaginary?

This project is based upon a question I asked myself in 2008 when I first took a Complex Variables course in college. From the observation of extending the pattern of this simple exercise in the textbook of computing \( (1+i)(2+i)(3+i) \) I was able to articulate a simple problem that ends up having an elaborate and interesting solution.

What's Included

• A 17-page PDF with scaffolded questions and full solutions, typeset in LaTeX
• Detailed solutions with illustrations
• Desmos graph link

Perfect For

• Algebra II Imaginary Numbers
• Precalculus
• AP Calculus classes
• College Calculus projects

File Format & Delivery

The download is a high-quality PDF typeset in LaTeX. After a successful purchase, you will receive a secure download link instantly via email.