Answer:
a)
[tex]20+9i[/tex]
b)
[tex]3+5i[/tex]
c)
[tex]19+17i[/tex]
d)
[tex]12+10i[/tex]
Step-by-step explanation:
a) The sum/difference of two complex numbers is given by:
[tex](a\pm bi)+(c\pm di)=a\pm c\pm(b\pm d)i[/tex]
so:
[tex](13+4i)+(7+5i)=13+4i+7+5i=20+9i[/tex]
b) Using the previous property and the distributive property:
[tex](5-i)-2*(1-3i)=5-i-2+6i=3+5i[/tex]
c)
Using a process similar to the previous one and taking into account that:
[tex]i=\sqrt{-1}[/tex]
[tex](3-i)(4+7i)=12+21i-4i+7=19+17i[/tex]
d) Using everything we used in the previous problems:
[tex](3-i)(4+7i)-i(5-i)-2(1-3i)i=19+17i-5i-1-2i-6=12+10i[/tex]
