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let z = cosa + i sina, then summation of z 2m-1 from m=1 to 15 at a=2 is what ???? Please give detailed, explained answer. thank you....

let z = cosa + i  sina, then summation of z 2m-1 from m=1 to 15 at a=2 is what ????


Please give detailed, explained answer.


thank you....

Grade:12

2 Answers

piyush garg
9 Points
12 years ago

z=e^ia in euler form

Z^(2m-1)=e^(2m-1)i

 summmission of cos(2m-1)a+isin(2m-1)a from m to 1 to 15

cos(1+2....................................29)a+isin (1+2...............................29)a   

cos(225a) +isin(225a)

put a=2

cos(450)+isin(450)

=i ans.

 

 

arpit agrawal
31 Points
10 years ago

Z=COSA+i sinA  

=e^iA  (euclid's eq.)

SUMMATION OF Z^2m-1 =   e^(iA)(2*1-1) + it wil form G.P

 

                 ANS ----------(e^2i)(e^60i -1)/(e^4i -1) 

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