Question

Комплексное число -√3/2+1/2i в тригонометрической форме имеет вид
a. 2*(cos(π/6))+ isin((π/6))
b.cos(5π/6)+isin(5π/6)
c. cos(5π/6)+isin(5π/6)

Answer 1

$z=- \frac{ \sqrt{3} }{2} + \frac{1}{2}i\\\\|z|= \sqrt{(- \sqrt{3}/2)^2+(1/2)^2 }= \sqrt{3/4+1/4}= \sqrt{1}=1\\\\cos \alpha = \frac{- \sqrt{3}/2 }{1}=- \sqrt{3}/2\\sin \alpha = \frac{1/2}{1}=1/2 \; \; \; \; \; \; \; \; \; \; \; \; \; \; =\ \textgreater \ \alpha = \frac{5 \pi }{6}\\\\z=|z|(cos \alpha +i*sin \alpha )\\\\z=1*(cos \frac{5 \pi }{6}+i*sin \frac{5 \pi }{6})=(cos \frac{5 \pi }{6}+i*sin \frac{5 \pi }{6})$