Question

Determinati partea reala a numarului complex z=(2/1+i) totul la puterea a5a

Answer 1

Amplificam cu conjugata, [tex] \frac{2}{1+i}= \frac{2(1-i)}{2}=1-i= \sqrt{2}( \frac{ \sqrt{2} }{2}-i\frac{ \sqrt{2} }{2})= \sqrt{2}(cos \frac{7 \pi }{4}+isin \frac{7 \pi }{4})[/tex]. $z^{5}=4 \sqrt{2}[cos( \frac{35 \pi }{4})+isin ( \frac{35 \pi }{4})],$
Partea reala este 4$\sqrt{2}cos(8 \pi + \frac{3 \pi }{4})=4 \sqrt{2}cos( \frac{3 \pi }{4})=-4 \sqrt{2} \frac{ \sqrt{2} }{2}=-4$