IIT JEE , AIEEE Forum - Mathematics , Algebra

sid.shah.90

If n is a positive integer, prove that

$|Im(z^{n})| \leq n|Im(z)|\|z|^{n-1}$

anant_c

hsbhatt

If x = r cis

Then we are being asked to prove that sinn

nsin

which can easily be proved by induction.

anant_c

EDIT:make that |sin(nx)|<=n|sin(x)|

ayshwarya

hey frnd if v take Z=Cisteta den lhs = Sin^2teta & rhs =n I Sinteta I

now v know dat -1<=Sinteta <=1 den as v konw dat

4 0< x<1 x^2
rate if useful

ayshwarya

hey print mistake its x^2 <=x hence as here x=I Sinteta I den x^2 is also <=nx for some n an integer