Complex Numbers 16 Proof of De Moivres Theorem by Induction

You’ll learn

• Prove De Moivre's theorem for n ∈ ℕ using the four-step induction structure
• Substitute the inductive hypothesis and expand the product using i² = −1
• Collapse the trig products with the page-14 formulas cos(A+B) and sin(A+B)
• Write the explicit induction conclusion — it carries marks of its own