Answer:
D. -35+13i
Step-by-step explanation:
We have the expression [tex](5+3i)-(5+3i)(5-5i)[/tex], first we have to solve:
[tex](5+3i)(5-5i)[/tex] we have to apply distributive property.
Distributive property: [tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
Then,
[tex](5+3i)(5-5i)=5.(5)+5.(-5i)+3i.(5)+3i.(-5i)\\(5+3i)(5-5i)=25-25i+15i-15i^2\\(5+3i)(5-5i)=25-10i+15\\(5+3i)(5-5i)=(40-10i)[/tex]
Observation: [tex]i^2=(-1)[/tex] then [tex]-15i^2=-15.(-1)=15[/tex]
Now replacing [tex](5+3i)(5-5i)=(40-10i)[/tex] in [tex](5+3i)-(5+3i)(5-5i)[/tex]:
[tex](5+3i)-(40-10i)=5+3i-40+10i=(5-40)+(3i+10i)=-35+13i[/tex]
Then the correct answer ir: D. -35+13i
