Question

1. Найдите область опр функции
У= 1-х/log3(x^2-9)

2. Запишите в тригонометрической форме число
z= √3/2 - 1/2i

Answer 1

$1); ; y=frac{1-x}{log_3(x^2-9)}; ,; ; OOF:; ; left { {{log_3(x^2-9)ne 0} atop {x^2-9 textgreater 0}} right. ; left { {{x^2-9ne 1} atop {(x-3)(x+3) textgreater 0}} right. \\ left { {{x^2ne 10} atop {xin (-infty ,-3)cup (3,+infty )}} right. ; left { {{xne pm sqrt{10}} atop {xin (-infty ,-3)cup (3,+infty )}} right. ; Rightarrow \\xin (-infty ,-sqrt{10})cup (-sqrt{10},-3)cup (3,sqrt{10})cup (sqrt{10},+infty )$

$2); ; z=frac{sqrt3}{2}-frac{1}{2}i\\|z|=sqrt{frac{3}{4}+frac{1}{4}}=1; ,\\argz=arctgfrac{-1/2}{sqrt3/2}=-arctgfrac{1}{sqrt3}=-frac{pi}{6}\\z=cos(-frac{pi}{6})+isin(-frac{pi}{6})$