簡約 (cos(x)+isin(x))^4

解

簡約

(cos (x) + i sin (x))^{4}

(cos^{4} (x) + 7 sin^{4} (x) - 6 sin^{2} (x)) + sin (4 x) i

解答ステップ

(cos (x) + i sin (x))^{4}

拡張

(cos (x) + i sin (x))^{4} : cos^{4} (x) + 4 i cos^{3} (x) sin (x) - 6 cos^{2} (x) sin^{2} (x) - 4 i sin^{3} (x) cos (x) + sin^{4} (x)

= cos^{4} (x) + 4 i cos^{3} (x) sin (x) - 6 cos^{2} (x) sin^{2} (x) - 4 i sin^{3} (x) cos (x) + sin^{4} (x)

標準的な複素数形式で書き直す:

(cos^{4} (x) + 7 sin^{4} (x) - 6 sin^{2} (x)) + sin (4 x) i

= (cos^{4} (x) + 7 sin^{4} (x) - 6 sin^{2} (x)) + sin (4 x) i