Roots of Complex Numbers (8.6.2)

Question 1

• Review: A complex number in polar form is expressed as r(cosθ + i sinθ), where r is the absolute value of the number and θ is its angle from the x-axis.

Answer 1

• Review: A complex number in polar form is expressed as r(cosθ + i sinθ), where r is the absolute value of the number and θ is its angle from the x-axis.

Question 2

• You can raise a complex number z in polar form to any power n using DeMoivre’s theorem: z^n = r^n [cos(nθ) + isin(nθ)].

Answer 2

• You can raise a complex number z in polar form to any power n using DeMoivre’s theorem: z^n = r^n [cos(nθ) + isin(nθ)].

Question 3

• Also use DeMoivre’s theorem to find the nth roots of a complex number in polar form. The nth roots of the complex number z = r (cosθ + i sinθ) are given by the formula .

Answer 3

• Also use DeMoivre’s theorem to find the nth roots of a complex number in polar form. The nth roots of the complex number z = r (cosθ + i sinθ) are given by the formula .