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Exercicios resolvidos James Stewart vol. 2 7ª ed - ingles

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APPENDIX H COMPLEX NUMBERS 0 361<br />

43. Using Euler's formula (6) with y= i· we have ei"/ 3 = cos i + isin i = ~ + '!] i.<br />

47. Taker = 1 and n = 3 in De Moivre'sTheorem to get<br />

(l(cos (} + i sin IJ)] 3 = 1 3 (cos 39 + i sin31J)<br />

(cos IJ + isin 0) 3 = cos 31J + i sin30<br />

cos 3 (} + 3(cos 2 fJ)(i sin 0) + 3(cos IJ)(isln 1J? + (i sin IJ) 3 =cos 38 + i s_in3fJ<br />

cos 3 1J + (3 cos 2 f) sin fJ)·i - 3 cos IJ sin 2 ()- (sin 3 fJ)i =cos 31J + i sin 31J<br />

( cos 3 1J - 3 sin 2 f) cos IJ) + (3 sin f) cos 2 f) - sin 3 1J)i = cos 30 + i ~in 3(}<br />

Equating real and imaginary parts gives cos 30 = cos~ fJ - 3 sin 2 () cos IJ and sin 3B = 3 sin IJ cos 2 (} - sin 3 e.<br />

49. F (x) = er:r: = e<br />

F'(x) = (eax cosbx)' + i(e

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