Question

Two square roots for 121(cos315° + i sin315°) are ?

Answer 1

Please help me :|

Answer 2

121^(1/2) to get 11 faster :)

Answer 3

but how to keep going from there?

Answer 4

i mean we knows that : z = 11 cis (157.5degrees + 180degrees k) how to find w0 and w1 ?

Answer 5

hmmm in class i learned a totally different way compare to what you did here ^^

Answer 6

let me write it out and you see it, because i don't get it :(

Answer 7

so with this example : The 3 cube roots of z = 8(cos60°+ i sin60°)

Answer 8

are you looking for the square root of
\[121\left(\cos(315)+i\sin(315)\right)\]?

Answer 9

i don't think so no

Answer 10

that looks like the question you asked yes?

Answer 11

or was the original question something different?

Answer 12

step 1 : wk = 8^1/3 cis (60°/3 + 360° k) according to the formula

Answer 13

step 2 : =2 cis(20°+120°k)

Answer 14

what was the original question for this ??

Answer 15

where k = 0,1,2. and they start to find w0 =, w1=,w2= .... and i don't get how they do that

Answer 16

Two square roots for 121(cos315° + i sin315°) are ? <---- this was original

Answer 17

I know that I am right till here--> z=121(1/sqrt(2) - i(1/sqrt(2)) )

Answer 18

ok so we can do that easy
first take the square root of 121, get 11
then divide the angle by 2 get
\[11\left(\cos(157.5)+i\sin(157.5)\right)\] for one answer. the other answer is half way around the unit circle

Answer 19

yes yes, i got the samething yay! :) the other answer is 180

Answer 20

couldn't you just put it together for a simpler form like : 11 cis (157.5 + 180k) ?

Answer 21

so start again with
\[121\left(\cos(315)+i\sin(315)\right)\] add 360 to the angle get
\[121\left(\cos(675)+i\sin(675)\right)\]take half of that angle and get your other solution
\[11\left(\cos(337.5)+i\sin(337.5)\right)\]

Answer 22

wait what? =.=

Answer 23

sure you can do what you wrote, but there are only two

Answer 24

i thought it was 180

Answer 25

it is not 180 it is what you wrote, \(157.5+180\)

Answer 26

ohh so you added them together

Answer 27

this is what you wrote
11 cis (157.5 + 180k)
and you only need k = 0 which gives 157.5 and k = 1 which gives 337.5

Answer 28

after that you are just going around the circle again so all the numbers repeat. there are only two square roots

Answer 29

wait wait, i think the answer need to be in trigonometric form

Answer 30

i wrote the answer in trig form above. there are two square roots.
\[11\left(\cos(157.5)+i\sin(157.5)\right)\] and
\[11\left(\cos(337.5)+i\sin(337.5)\right)\]

Answer 31

those are the answers ?

Answer 32

@satellite73 , he is looking for the values

Answer 33

yes those are the two answers

Answer 34

I think he is looking for this method --> http://answers.yahoo.com/question/index?qid=20081102074555AAAJbwx

Answer 35

oh lol, what about if there were 3 answers? what do you do to find the third one ?

Answer 36

@shivam_bhalla i doubt that. there is no way in the world he is going to be able to evaluate those, unless you are going to use some half angle formulas. it is doable, but he said "trig form" so those are the answers

Answer 37

@Ala123 there will be three answers if you are looking for cube roots

Answer 38

@shivam_bhalla : satellite73 method is just like in my book ^^

Answer 39

4 answers for 4th roots, etc

Answer 40

Great. Good work :)

Answer 41

cool, i get it now thanks guys !

Answer 42

now let me try cube root and i'll be back asking for help again =.=