Question

решите плиз, срочно нужно!!!

Answer 1

$2.;frac{2+3i}{1-2i}=a(2+3i)+b(1-2i)\2+3i=a(2+3i)(1-2i)+b(1-2i)^2\2+3i=a(8-i)+b(-3-4i)\2+3i=8a-ai-3b-4bi\2+3i=(8a-3b)+(-a-4b)i\begin{cases}-a-4b=3\8a-3b=2end{cases}Rightarrowbegin{cases}a=-3-4b\-24-32b-3b=2end{cases}Rightarrowbegin{cases}a=-frac1{35}\b=-frac{26}{35}end{cases}$

$3.;z=frac{-41+63i}{50}-frac{6i+1}{1-7i}=frac{(-41+63i)(1-7i)-50(6i+1)}{50(1-7i)}=\=frac{-41+350i-441i^2-300i-50}{50(1-7i)}=frac{-91+441+50i}{50(1-7i)}=frac{350+50i}{50(1-7i)}=frac{50(7+i)}{50(1-7i)}=frac{7+i}{1-7i}\frac{7+i}{1-7i}=a+bi\7+i=(a+bi)(1-7i)\7+i=(a+7b)+(-7a+b)i\begin{cases}a+7b=7\-7a+b=1end{cases}Rightarrowbegin{cases}a+7+49a=7\b=1+7aend{cases}Rightarrowbegin{cases}a=0\b=1end{cases}Rightarrow\\z=i$