Answer:
Part 1) [tex](6 + 3i)(6-3i)=45[/tex]
Part 2) [tex](4 -5i)(4+5i)=41[/tex]
Part 3) [tex](-3+8i)(-3-8i)=73[/tex]
Step-by-step explanation:
we know that
The formula of the difference of squares is equal to
[tex](a-b)(a+b)=a^2-b^2[/tex]
Part 1) we have
[tex](6 + 3i)(6-3i)[/tex]
Applying difference of squares
[tex](6 + 3i)(6-3i)=6^2-(3i)^2[/tex]
Remember that
[tex]i^{2}=-1[/tex]
[tex](6 + 3i)(6-3i)=36-(9)(-1)[/tex]
[tex](6 + 3i)(6-3i)=36+9[/tex]
[tex](6 + 3i)(6-3i)=45[/tex]
Part 2) we have
[tex](4 -5i)(4+5i)[/tex]
Applying difference of squares
[tex](4 -5i)(4+5i)=4^2-(5i)^2[/tex]
Remember that
[tex]i^{2}=-1[/tex]
[tex](4 -5i)(4+5i)=16-(25)(-1)[/tex]
[tex](4 -5i)(4+5i)=16+25[/tex]
[tex](4 -5i)(4+5i)=41[/tex]
Part 3) we have
[tex](-3+8i)(-3-8i)[/tex]
Applying difference of squares
[tex](-3+8i)(-3-8i)=(-3)^2-(8i)^2[/tex]
Remember that
[tex]i^{2}=-1[/tex]
[tex](-3+8i)(-3-8i)=9-(64)(-1)[/tex]
[tex](-3+8i)(-3-8i)=9+64[/tex]
[tex](-3+8i)(-3-8i)=73[/tex]
