Выполните действия с комплексными числами:
1)
frac {(-3-i)(3-i)}{(3+i)(3-i)}=-1" title="frac {(i-1)(1+2i)}{3+i}=frac{(i+2i^2-1-2i)(3-i)}{(3+i)(3-i)}=
frac {(-3-i)(3-i)}{(3+i)(3-i)}=-1" alt="frac {(i-1)(1+2i)}{3+i}=frac{(i+2i^2-1-2i)(3-i)}{(3+i)(3-i)}=
frac {(-3-i)(3-i)}{(3+i)(3-i)}=-1" />
2)
-frac{(5+25i-i-5i^2)(5-12i)}{(5+12i)(5-12i)}=
-frac {(10+24i)(5-12i)}{(5+12i)(5-12i)}=
-frac {2(5+12i)(5-12i)}{(5+12i)(5-12i)}=-2" title="frac{(5-i)(1+5i)}{-5-12i}=
-frac{(5+25i-i-5i^2)(5-12i)}{(5+12i)(5-12i)}=
-frac {(10+24i)(5-12i)}{(5+12i)(5-12i)}=
-frac {2(5+12i)(5-12i)}{(5+12i)(5-12i)}=-2" alt="frac{(5-i)(1+5i)}{-5-12i}=
-frac{(5+25i-i-5i^2)(5-12i)}{(5+12i)(5-12i)}=
-frac {(10+24i)(5-12i)}{(5+12i)(5-12i)}=
-frac {2(5+12i)(5-12i)}{(5+12i)(5-12i)}=-2" />
3)
frac {15+25i}{9-25i^2}+frac {15-25i}{9-25i^2}=
frac{15+25i}{9+25}+frac {15-25i}{9+25}=
frac{15+25i+15-25i}{34}=
frac {30}{34}=frac {15}{17}" title="frac{5}{3-5i}+frac {5}{3+5i}=
frac {15+25i}{9-25i^2}+frac {15-25i}{9-25i^2}=
frac{15+25i}{9+25}+frac {15-25i}{9+25}=
frac{15+25i+15-25i}{34}=
frac {30}{34}=frac {15}{17}" alt="frac{5}{3-5i}+frac {5}{3+5i}=
frac {15+25i}{9-25i^2}+frac {15-25i}{9-25i^2}=
frac{15+25i}{9+25}+frac {15-25i}{9+25}=
frac{15+25i+15-25i}{34}=
frac {30}{34}=frac {15}{17}" />
4)
frac{2-i}{4-i^2}+frac {2+i}{4-i^2}=
frac{2-i}{4+1}+frac {2+i}{4+1}=
frac {2-i+2+i}{5}=frac {4} {5}" title="frac {1}{2+i}+frac {1}{2-i}=
frac{2-i}{4-i^2}+frac {2+i}{4-i^2}=
frac{2-i}{4+1}+frac {2+i}{4+1}=
frac {2-i+2+i}{5}=frac {4} {5}" alt="frac {1}{2+i}+frac {1}{2-i}=
frac{2-i}{4-i^2}+frac {2+i}{4-i^2}=
frac{2-i}{4+1}+frac {2+i}{4+1}=
frac {2-i+2+i}{5}=frac {4} {5}" />
5)
frac {(3-i)^2}{9-i^2}+frac {(3+i)^2}{9-i^2}=
frac{9-6i+i^2+9+6i+i^2}{9+1}=
frac {16}{10}=frac {8}{5}=1,6" title="frac {3-i}{3+i}+frac {3+i} {3-i}=
frac {(3-i)^2}{9-i^2}+frac {(3+i)^2}{9-i^2}=
frac{9-6i+i^2+9+6i+i^2}{9+1}=
frac {16}{10}=frac {8}{5}=1,6" alt="frac {3-i}{3+i}+frac {3+i} {3-i}=
frac {(3-i)^2}{9-i^2}+frac {(3+i)^2}{9-i^2}=
frac{9-6i+i^2+9+6i+i^2}{9+1}=
frac {16}{10}=frac {8}{5}=1,6" />
6)
frac {(4-5i)(4-i)}{16-i^2}+frac {(4+5i)(4+i)}{16-i^2}=
frac{16-4i-20i+5i^2+16+4i+20i+5i^2}{16+1}=
frac {22}{17}" title="frac {4-5i}{4+i}+frac {4+5i}{4-i}=
frac {(4-5i)(4-i)}{16-i^2}+frac {(4+5i)(4+i)}{16-i^2}=
frac{16-4i-20i+5i^2+16+4i+20i+5i^2}{16+1}=
frac {22}{17}" alt="frac {4-5i}{4+i}+frac {4+5i}{4-i}=
frac {(4-5i)(4-i)}{16-i^2}+frac {(4+5i)(4+i)}{16-i^2}=
frac{16-4i-20i+5i^2+16+4i+20i+5i^2}{16+1}=
frac {22}{17}" />
