Question

De Moivre's theorem: Use de Moivre's Theorem to find the following expression. Write your answer in standard form.
(-sqrt3 + i)^4... someone look over my work and tell me what I am doing wrong??!!

Answer 1

The answer is pizza, it always has been it always will be

Answer 2

= 2(cos 30 + i sin30)^4 = 16(cos120 + i sin120) = 16(-1/2 + sqrt3 /2 i) = -8+8sqrt3i

Answer 3

IT WILL ALWAYS BE PIZZA

Answer 4

ALWAYS

Answer 5

jim_thompson5910 can u look over this? please?

Answer 6

notice how we have -sqrt(3) and 1 from -sqrt3 + i = -sqrt3 + 1i

if you divide each by 2 to get -sqrt(3)/2 and 1/2. Those two values are found on the unit circle

Answer 7

Let's make z = -sqrt(3) + i

divide everything by 2 to get z/2 = -sqrt(3)/2 + (1/2)i

Answer 8

then compare -sqrt(3)/2 + (1/2)i to cos(theta) + i*sin(theta)

what must the value of theta be?

Answer 9

wow hold on i lost u

Answer 10

sorry about that

where are you stuck?

Answer 11

ok why would you divide it by two?

Answer 12

-sqrt(3) is not found on the unit circle

but -sqrt(3)/2 is found on the unit circle

Answer 13

dividing by 2 and comparing lets you avoid calculator in computing the angle

Answer 14

ok, can someone write it out for me? because I am not getting it... You cant just randomly divide two to avoid computing, so I am sure you are saying something that makes a lot of sense to you guys but for me is in another language

Answer 15

are you allowed to use calculator ?

Answer 16

if so find the angle of \(a+ ib \) by the usual formula
\[\theta = \tan^{-1}\left(\frac{b}{a}\right)\]

Answer 17

the angle you have calculated in the start was wrong, work it again

Answer 18

i did ... isnt it 120?

Answer 19

ok let me see...