Transcript Section 6.6: DeMoivre’s Theorem and the Nth Roots

March 18, 2015

A complex number, a + bi, can be
plotted as (a, b).
Example: Plot the following points…
a) 3 – 2i
b) 5i – 1
c) 7
d) -4i
a
+ bi = r ( cos θ + i sin θ) where r
2
2
r

a

b
(modulus) can be found using
and θ (angle) can be found using b = r sin θ.
a)
b)
Find in standard form, a + bi.
a)
7(cos 60° + i sin 60°)
b)
15 (cos 315° + i sin 315°)
 To
multiply complex numbers, multiply
moduli, and add angles.
 To
divide complex numbers, divide
moduli, and subtract angles.
Given a = 15 (cos 900° + i sin 900°) and
b = 3(cos 30° + i sin 30°), find the product
and quotient of these two complex
numbers.
 DeMoivre’s
=
Theorem: [r
(cos   isin  )]
r (cos n  i sin n )
n
n