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qn. (1 Viewer)
- Thread starter bos1234
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ssglain
Member
a) Remember the double angle results for sine and cosine.
LHS = -2isin(n@/2)*[cos(n@/2)+isin(n@/2)]
= -2isin(n@/2)cos(n@/2) + 2[sin(n@/2)]^2
= -isin(n@) + [1 - cos(n@)]
= 1 - [cos(n@) + isin(n@)] = RHS as required.
b) I think you're missing some vital information - e.g. 'z is the nth root of unity' is typical, in which case this is really a 2U G.P. question.
a = z, r = z
S(n) = a[(r^n) - 1]/(r - 1)
= z[(z^n) - 1]/(z - 1)
= 0 {because z^n = 1}
LHS = -2isin(n@/2)*[cos(n@/2)+isin(n@/2)]
= -2isin(n@/2)cos(n@/2) + 2[sin(n@/2)]^2
= -isin(n@) + [1 - cos(n@)]
= 1 - [cos(n@) + isin(n@)] = RHS as required.
b) I think you're missing some vital information - e.g. 'z is the nth root of unity' is typical, in which case this is really a 2U G.P. question.
a = z, r = z
S(n) = a[(r^n) - 1]/(r - 1)
= z[(z^n) - 1]/(z - 1)
= 0 {because z^n = 1}