Question

Convert to a+bi form.
(2cos20 degrees + 2 i sin20 degrees) ^3

Answer 1

@Mertsj

Answer 2

i have no clue where to start, im so lost.

Answer 3

I think it may be posted wrong. There should be an "i" in there somewhere.

Answer 4

yes sorry ive corrected it

Answer 5

Take the two out.

Answer 6

ok

Answer 7

\[2(\cos 20+i \sin 20)\]

Answer 8

2(cos20 degrees + i sin20 degrees) ^3

Answer 9

yes

Answer 10

Now. Raise the 2 to the third power and multiply the argument by 3

Answer 11

so 8 times the whole thing in parentheses?

Answer 12

\[8(\cos 60+i \sin 60)\]

Answer 13

you just multiply? even though its raised to the power of 3?

Answer 14

ok and then?

Answer 15

\[8(\frac{1}{2}+i\frac{\sqrt{3}}{2})=4+4\frac{\sqrt{3}}{2}i\]

Answer 16

so then multiply the left side again?

Answer 17

oh whoop sorry never mind

Answer 18

No. Drop the 2. It should be
\[4+4\sqrt{3}i\]

Answer 19

I forgot. I had already cancelled the 2 into the 8

Answer 20

okay. thank you. but what if the question was like 4^i ? how would you solve it then

Answer 21

\[4^i\]

Answer 22

Like that?

Answer 23

yes, like that

Answer 24

http://www.wolframalpha.com/input/?i=simplify+4^i

Answer 25

log?? why log??

Answer 26

I think they mean natural log...ln

Answer 27

but still.. i dont understand why you use natural log?

Answer 28

actually i understand. what if the question was e^ (iπ)?

Answer 29

Have you had euler's equation?

Answer 30

yes

Answer 31

oh so cos π +i sinπ ?

Answer 32

http://www.wolframalpha.com/input/?i=simplify+e^%28i%CF%80%29

Answer 33

so negative , ok.

Answer 34

what if it was e^pi/2 i ?

Answer 35

Probably treat that like: