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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 ????
thank you....```
8 years ago

piyush garg
9 Points
```										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.

```
8 years ago
arpit agrawal
31 Points
```										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)
```
7 years ago
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