Применяем формулу Муавра:

[tex](3 - \sqrt{3}*i)^{15} = (\sqrt{3}*2)^{15} * (\frac{\sqrt{3} }{2} - \frac{1}{2} *i)^{15} =\\= 2^{15}*\sqrt{3}^{15}*( cos(\frac{11\pi }{6} ) + i*sin(\frac{11\pi }{6} ))^{15} = \\= 2^{15}*\sqrt{3}^{15}*( cos(\frac{11*15\pi }{6} ) + i*sin(\frac{11*15\pi }{6} )) =\\= 2^{15}*\sqrt{3}^{15}*( cos(\frac{55\pi }{2} ) + i*sin(\frac{55\pi }{2} )) =\\= 2^{15}*\sqrt{3}^{15}*( cos(27\pi + \frac{\pi }{2} ) + i*sin(27\pi +\frac{\pi }{2} )) = \\=2^{15}*\sqrt{3}^{15}*( -i) = - 2^{15}*\sqrt{3}^{15} *i[/tex]