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....

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.

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)