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Is it possible to find the value of the following?
10[(cos 75°+ i sin 75°)(cos 30° - i sin 30°)] / [(cos 30° + i sin 30°)(cos 30° - i sin 30°)]
3 Answers
- ?Lv 78 years agoFavorite Answer
10[(cos 75°+ i sin 75°)(cos 30° - i sin 30°)] / [(cos 30° + i sin 30°)(cos 30° - i sin 30°)]
= 10[(√3 - 1)/2√2) + [i(1 + √3) / 2√2)][(√3/2 - i (1/2)] / 1
= 10[(√3 - 1)/2√2) + [i(1 + √3) / 2√2)][0.866... - 0.5 i]
= (5√2)[(√3 - 1) + i(1 + √3)][0.866... - 0.5 i]
= 9.65926 - 2.58819i
- Anonymous8 years ago
cosA + isinA = e^(iA)
Using this formula and simplifying
the above expression becomes:
10e^(i45°) = 10(cos45° + isin45°)
= 5*2^1/2 + i 5*2^1/2
