Math Analysis:
Use Demoivre's theorem to simplify the expression. Write the answer in a + bi form
(4cis135)^4

Question

Math Analysis:
Use Demoivre's theorem to simplify the expression. Write the answer in a + bi form
(4cis135)^4

anonymous · Answer

(4cis135)^4=4^4(cos(135*4))

anonymous · Answer

is the answer -256?

anonymous · Answer

256(cos180)=-256

anonymous · Answer

got it?

anonymous · Answer

what about sine b/c it's "cis"

anonymous · Answer

i tought cis was a typo

anonymous · Answer

cis means cos(theta)+i*sin(theta)

anonymous · Answer

yea so the answer would just be -256 + 0i?

anonymous · Answer

oh.. then
256(cos180 +i sin180)=-256

anonymous · Answer

ya, it's pure real number

anonymous · Answer

Where is the 180 coming from?

anonymous · Answer

cos(135)=-root(2)/2

anonymous · Answer

idk. all i know is that the answer is -256

anonymous · Answer

no, from my teacher's work it's -256

anonymous · Answer

No, I meant cos135=+root(2)/2

anonymous · Answer

it wants the answer in a + bi form so i guess the 180 comes from multiplying the 135 by 4? o-o

anonymous · Answer

135)^4 which is really 135 x 4 is 180

anonymous · Answer

Hm...I've never seen that conversion to multiplication before

anonymous · Answer

135*4=540
540-360=180

anonymous · Answer

i know.. :\ idk but the right answer is -256 from my teacher's handouts

anonymous · Answer

oh yeah, sorry lol

anonymous · Answer

cos is a periodic function. So doesn't matter is angle is 180, 540, 900..... all same values of cos

anonymous · Answer

Right right, but wasn't the original problem 
$$(4cis135)^4$$

anonymous · Answer

So that means you would need to evaluate cis(135) and then multiply by 4

anonymous · Answer

don't confuse him. The proceedure is right. The angle is multiplied, not the cos of the angle!!

anonymous · Answer

4cis(135) doesn't mean that the angle is multiplied...

anonymous · Answer

this is a polar expretion of a comlex number

anonymous · Answer

5cos(0)=5
cos(5*0)=1

It's not the same thing.

anonymous · Answer

(4cis135)^4  is the problem

anonymous · Answer

Right

anonymous · Answer

Demoivre's theorem look in google

anonymous · Answer

Ah, quite right.  My bad.

anonymous · Answer

np

anonymous · Answer

Apologies.

anonymous · Answer

Write the complex number in trigonometric form, using degree measure for the argument.
23. -10 - 24i

anonymous · Answer

lol might as well post up my next question here o-o

anonymous · Answer

you should post a new question in new window

anonymous · Answer

gg k :)

anonymous · Answer