1 + i = (\(\sqrt{\quad}\)2)(cos 45°+ i sin 45°),
\(\sqrt{\quad}\)3 + i = 2((\(\sqrt{\quad}\)3)/2 + \(\frac{i}{2}\)) = 2(cos 30° + i sin 30°).
(1 + ｉ)/(\(\sqrt{\quad}\)3 + i) = (1/\(\sqrt{\quad}\)2)(cos(45 - 30)°+ i sin(45 - 30)°)
= (1/\(\sqrt{\quad}\)2)(cos 15° + i sin 15°).
(一方 (1 + ｉ)/(\(\sqrt{\quad}\)3 + i) = (1 + ｉ)(\(\sqrt{\quad}\)3 - i)/4
= (\(\sqrt{\quad}\)3 + 1 + (\(\sqrt{\quad}\)3 - 1)i)/4)

15n = 180 とすると n = 12.

((1 + ｉ)/(\(\sqrt{\quad}\)3 + i)\()^{13}\) + ((1 - ｉ)/(\(\sqrt{\quad}\)3 - i)\()^{13}\)
= (1/\(\sqrt{\quad}\)2\()^{13}\)(cos(13×15)°+ i sin(13×15°)
　　　　　　　　　　　　　　+ (cos(13×15)°- i sin(13×15)°)
= (1/(\(2^{6}\)・\(\sqrt{\quad}\)2))(2cos(180°+ 15°)
= -cos15°/32\(\sqrt{\quad}\)2
= -(\(\sqrt{\quad}\)3 + 1)(\(\sqrt{\quad}\)2)/(4・32\(\sqrt{\quad}\)2)
= -(\(\sqrt{\quad}\)3 + 1)/128.