QCEVault

Mathematical induction and trigonometric proofs — Question 266

Original QCE Vault practice · 6 marks

Q266 · Practice questionTechnology-freeComplex familiar6 marks

QUESTION 266 (6 marks)

Let θ∈R\theta\in\mathbb R. The angle addition identities may be used.
a)
Prove (cos⁡θ+isin⁡θ)n=cos⁡(nθ)+isin⁡(nθ)(\cos\theta+i\sin\theta)^n=\cos(n\theta)+i\sin(n\theta) for all positive integers n by mathematical induction.
[6 marks]
Question linkSyllabus coverage

Related questions

  1. Q178 · Original practice · 6 marks
    Consider (cos⁡θ+isin⁡θ)4(\cos\theta+i\sin\theta)^4.
    Mathematical induction and trigonometric proofs
  2. Q179 · Original practice · 6 marks
    For positive integers n, let Sn=∑k=1n(2k−1)3S_n=\sum_{k=1}^n(2k-1)^3.
    Mathematical induction and trigonometric proofs
  3. Q180 · Original practice · 6 marks
    For positive integers n, consider 8n−18^n-1.
    Mathematical induction and trigonometric proofs
  4. Q181 · Original practice · 6 marks
    A programmable light display contains k2kk2^k lights in row k, for k=1,…,nk=1,\ldots,n.
    Mathematical induction and trigonometric proofs