SME
Grade 12 Math
Polar coordinates and polar form of complex numbers
The main lesson, then each kind of problem it solves.
Polar coordinates and polar form of complex numbers
Main lesson
Polar form of a complex number
Use this for “Write 2(cos 60° + i sin 60°) as a + bi,” or back.
Multiplying in polar form
Use this for “Multiply 2(cos 30° + i sin 30°) by 3(cos 60° + i sin 60°).”
Powers by De Moivre’s theorem
Use this for “Find (1 + i)⁸ with De Moivre’s theorem.”
The nth roots of a complex number
Use this for “Find the cube roots of 8i” or “the fourth roots of −16.”
Rose curves
Use this for “How many petals does r = 4 cos 2θ have? Find r at θ = 30°.”
Limaçons and cardioids
Use this for “Find r on r = 2 + 2 cos θ at θ = 60°” and the curve’s shape.
Circles through the pole
Use this for “Graph r = 6 cos θ: find r at θ = 60°, the center and the radius.”
The spiral r = aθ
Use this for “Graph r = 0.5θ: find r at θ = 270°” or “At what angle is r = 6?”