Complex numbers

Worked examples (6)

• 1A power via modulus-argument form
• 2A power of a complex number not on the unit circle
• 3Proving de Moivre's theorem by induction
• 4The cube roots of unity
• 5The cube roots of a general complex number
• 6Using roots of unity to factorise an equation

Model answers (6)

• ✓Model answer 1
• ✓Model answer 2
• ✓Model answer 3
• ✓Model answer 4
• ✓Model answer 5
• ✓Model answer 6

Worked examples (6)

• 1cos 3θ in powers of cos θ
• 2sin 4θ in terms of sin θ and cos θ
• 3cos⁴θ as a sum of multiple angles
• 4Summing a cosine series with C + iS
• 5Deriving cos 5θ and solving an equation
• 6tan 3θ in terms of tan θ

Model answers (6)

• ✓Model answer 1
• ✓Model answer 2
• ✓Model answer 3
• ✓Model answer 4
• ✓Model answer 5
• ✓Model answer 6