a)
(5 + i)/3i=
5/3i + 1/3=
1/3 + 5i/3i²=
1/3-5i/3
b)
2 / (7 - i)=
2(7 + i)/(7 - i)(7 + i)=
(14 + 2i)/(49 - i²)=
(14 + 2i)/(49 + 1)=
(14 + 2i)/50=
14/50 + 2i/50=
7/25 + i/25
c)
((1 + 2i )/ (2 + i)) - 5=
(1 + 2i - 5(2 + i))/ (2 + i)=
(1 + 2i - 10 - 5i)/(2 + i)=
(- 9 - 3i)/(2 + i)=
(- 9 - 3i)(2 - i)/(2 + i)(2 - i)=
(- 18 - 9i - 6i + 6i²)/(4 - i²)=
(- 18 - 9i - 6i + 6i²)/(4 - i²)=
(- 19 - 15i)/(4 + 1)=
(- 19 - 15i)/5=
-19/5-3i
d)
((3 + i) / ( 4 + 2i)) + (5 - i)=
((3 + i) + (5 - i)( 4 + 2i))/ ( 4 + 2i)=
(3 + i + 20 + 10i - 4i - 2i²)/ ( 4 + 2i)=
(25 + 7i)/ ( 4 + 2i)=
(25 + 7i) ( 4 - 2i)/ ( 4 + 2i)( 4 - 2i)=
(100 + 50i + 28i - 14i²)/ ( 16 - 4i²)=
(114 + 78i)/ 20=
114/20 + 78i/20=
114/20+78i/20=
57/10 + 9i/2
J'espère que tu as compris
A+
