Question

1)Sa se calculeze:
a) (2-i) (4+i)
b) (5+3i) (5-3i)
c) (1+i) patrat
2) Sa se calculeze opusul si inversul numarului complex:
a) -2-i
b) 4-3i

Answer 1

2) a) -2-i opusul: 2+i
inversul: 1/-2-i
b) 4-3i opusul: -4+3i
inversul: 1/4-3i
1) a)(2-i)×(4+i)=2×4+2×i-i×4-i×i=
=8+2i-4i-(-1)=8-2i+1=-2i+9
b)(5+3i)×(5-3i)=5×5-5×3i+3i×5-3i×3i=
=25-15i+15i-9×(-1)=25+9=34
c) (1+i)^2=1^2+2×1×i+i^2=1+2i+(-1)=2i