Pratham Ashish
Last Activity: 15 Years ago
hi,
consider the eq.
x n -1 = 0
this eq. will have n roots, which will be the n th roots of unity,
x n = 1
x n = e i2¶k
x = e i2¶k/n
where k goes from 0 to n-1
x= 1, e i2¶/n ,e i4¶/n ,e i6¶/n .............................e i2 (n-1)¶/n
from the analysis of eq . we can tell that sum of all the roots will be 0 ,becoz the coeff. of x^(n-10 is zero here
so,
1+e i2¶/n +e i4¶/n +e i6¶/n ............................+.e i2 (n-1)¶/n =0
e i2¶/n +e i4¶/n +e i6¶/n ............................+.e i2 (n-1)¶/n = -1 hence proved
(ii)
sin nØ = b0 + b1 sinØ + b2 sin2Ø + b3 sin3Ø.................................+ bn sin nØ
in this case , we can find the values of b0 ,b1, b2.......... by succesive differentiation of both the
sides & then putting Ø =0 , in that eq.
for b0,
put Ø = 0 , we get
b0 =0
for b1,
on diff. both the sides & then putting Ø = 0, we get
b1 = n
for furthur coeff. we have to do furthur diff.
