Question

Use DeMoivre's Theorem to find the fourth roots of: 16(cos(4pi/3) + isin(4pi/3))

Answer 1

divide by 4

Answer 2

well divide the angle by 4, also take the fourth root of 16, which is 2

Answer 3

easy right?

Answer 4

the angle

Answer 5

which in this case is real real easy since
\[\frac{4\pi}{3}\div 4=\frac{\pi}{3}\]

Answer 6

after that you have a choice

Answer 7

This thm comes from eulers identity

Answer 8

you can divide up the unit circle in two 4 equal parts, with one at \(\frac{\pi}{3}\) or you can keep adding \(2\pi\) and dividing
first method is loads easier

Answer 9

ok i got it, but how would i use the thrm because my teacher marks points off if we dont what the directions says. @satellite73

Answer 10

*if we dont do what the directions says

Answer 11

can you help @dan815

Answer 12

yea what do u need

Answer 13

i have to use the demoivres thrm, but idk how?

Answer 14

oky it comes from eulers identity

Answer 15

idk what that is

Answer 16

okay u need some basic stuff first

Answer 17

There is a way to write a linear transformation matrix in terms of a multiplication of complex numbers

Answer 18

complex numbers are quite useful in this area to figure out rotations and scaling

Answer 19

so first thing u shud know is

Answer 20

if u have a vectors
<1,1> & <1,2> lets say