Question

(1+i)×(1-i)¹⁵ вычислить комплексное число в виде тригонометрической записи

Answer 1

Ответ:

$(1 + i)(1 - i)^{15} = \\ \\ = \sqrt{2} (cos( \frac{\pi}{4} ) + i \times sin( \frac{\pi}{4} )) \times ( \sqrt{2} (cos( \frac{7\pi}{4} ) + i \times sin( \frac{7\pi}{4} )))^{15} = \\ \\ = \sqrt{2} (cos( \frac{\pi}{4} ) + i \times sin( \frac{\pi}{4} )) \times 128 \sqrt{2} (cos( \frac{\pi}{4} ) + i \times sin( \frac{\pi}{4} )) = \\ \\ = \sqrt{2} \times 128 \sqrt{2} (cos( \frac{\pi}{4} + \frac{\pi}{4} ) + i \times sin( \frac{\pi}{4} + \frac{\pi}{4} )) = \\ \\ = 256(cos( \frac{\pi}{4} + \frac{\pi}{4} ) + i \times sin( \frac{\pi}{4} + \frac{\pi}{4} )) = \\ \\ = 256(cos( \frac{\pi}{2} ) + i \times sin( \frac{\pi}{2} ))$