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TOPICS COVERDED IN THIS VIDEO
In this video, we solve a **beautiful and surprising problem from complex numbers**.

Given:
zₙ = cos(π / 2ⁿ) + i sin(π / 2ⁿ)

we prove that the infinite product:
z₁ · z₂ · z₃ · … = −1

Using Euler’s formula and properties of arguments, we carefully analyze how multiplying complex numbers affects magnitude and angle.
Step by step, the infinite product simplifies and leads to the unexpected but elegant result **−1**.

✨ What you will learn in this video:
• Representation of complex numbers in trigonometric form
• Infinite products of complex numbers
• Role of arguments and convergence
• Why the product converges to −1
• How beauty appears in higher mathematics

This video is ideal for:
✔ Class 11–12 Mathematics
✔ BSc Mathematics (Complex Analysis basics)
✔ Olympiad and competitive exams
✔ Students who love mathematical beauty

🎓 Channel: mediate TO math (mTm)
💡 Learn visually. Understand deeply. Love mathematics.

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