Roots of Complex Numbers (8.6.2) Flashcards Preview

Pre-Calculus > Roots of Complex Numbers (8.6.2) > Flashcards

Flashcards in Roots of Complex Numbers (8.6.2) Deck (3)
Loading flashcards...
1
Q

• 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.

A

• 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.

2
Q

• 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)].

A

• 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)].

3
Q

• 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 .

A

• 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 .

Decks in Pre-Calculus Class (343):