© examsiri.com
Question : 10 of 160
Marks:
+1,
-0
Solution:
Given,
n,K∈N such that
n≠3KLet
z=√3+i, then
z=√3−i‌|z|=|z|=√3+1=2‌arg(z)=tan−1(‌)=‌‌arg(z)=tan−1(−‌)=‌‌∴‌‌z=2(cos‌+isin‌‌)‌⇒z2n=22n(cos‌+isin‌‌)‌‌ And ‌z=2(cos‌−isin‌‌)‌⇒z2n=22n(cos‌−isin‌‌)‌∴z2n+z2n=2⋅22n‌cos(‌)‌=22n+1‌cos(‌)Since,
n≠3K⇒n is not a multiple of
3‌cos(‌)≠cos(kπ)=±1=(−1)n+122n
© examsiri.com
Go to Question: