De Moivre's Thereom Question

eirebhoy

When answering a question on de Moivres Thereom, how do you know if you have to add 2npie because sometimes you don't have to add it.

BTW. I haven't got the symbol for pie but you know what I mean.

Raptor

If its question im thinking of (z^6 = 1, find some of the roots or something similiar) the ya use the n value to find different roots.

E.g. z^3 =1, find 3 roots

Z^3 = (Cos (pie)+iSin(pie) ) because cos pie = 1 and sin pie = o

Thus z = (cos (pie) + iSin (pie))^(1/3)

z = (cos (2npie+pie) + iSin (2npie+pie))^(1/3)

Then you put in different values of n to find the different roots, n=0 n=1 etc. Eventually the roots will start repeating themselves (in this case there are 3 roots as z is to the power of 3) You will/should be told how many roots you need to find

Of course if this ISNT the question, it prolly wont be much help

StickyMcGinty

only add 2npie when the degree isn't in the quadrant you want (all, sin,cos, tan).

adding 2npie doesnt change the degree at all at all


what a sh1te explaination, hang on till i look for an easier way to explain it

Raptor

If its question im thinking of (z^6 = 1, find some of the roots or something similiar) the ya use the n value to find different roots.

E.g. z^3 =1, find 3 roots

Z^3 = (Cos (pie)+iSin(pie) ) because cos pie = 1 and sin pie = o

Thus z = (cos (pie) + iSin (pie))^(1/3)

z = (cos (2npie+pie) + iSin (2npie+pie))^(1/3)

z = (cos (2npie+pie)/3 + iSin (2npie+pie)/3)

Then you put in different values of n to find the different roots, n=0 n=1 etc. Eventually the roots will start repeating themselves (in this case there are 3 roots as z is to the power of 3) You will/should be told how many roots you need to find

Of course if this ISNT the question, it prolly wont be much help Post a reply and ill see if i can help more

ella minnow pea

mmmmmmmmmmmmmmmmmmmm pie