Question:
What is the value of [( i + √3) / 2]2019 + [( i - √3) / 2]2019?
What is the value of [( i + √3) / 2]2019 + [( i - √3) / 2]2019?
Options:
- 2i
- -2i
- -1
- 1
- 2i
- -2i
- -1
- 1
Correct Answer: a)
Explanation:
‘ iy32019 Nn i y372019
1 2 2 1
h VB 1.72019 VB q.72019 ‘
1 = 7 +3 5-3 1
hon a
‘ cos § +isin I 2009 _ cos 5 — isin 7 2019 ‘
‘ = cos 209 4 sin 209% _ cog 209 4 j sin 20307
1 by De-Moi√re’s theorem, (cos 6 + i sin 0)” =cos nf + isinné
=2isin 20 ‘
‘ = 2isin(168 x 2m + 37) ‘
= 2isin 32
‘ ‘. sin (2n7 + 6) = sin 6, n is an integer ‘
‘ =2isin% =2
‘ iy32019 Nn i y372019
1 2 2 1
h VB 1.72019 VB q.72019 ‘
1 = 7 +3 5-3 1
hon a
‘ cos § +isin I 2009 _ cos 5 — isin 7 2019 ‘
‘ = cos 209 4 sin 209% _ cog 209 4 j sin 20307
1 by De-Moi√re’s theorem, (cos 6 + i sin 0)” =cos nf + isinné
=2isin 20 ‘
‘ = 2isin(168 x 2m + 37) ‘
= 2isin 32
‘ ‘. sin (2n7 + 6) = sin 6, n is an integer ‘
‘ =2isin% =2