Answer:
Distributive property says that:
[tex]a \cdot (b+c) =a\cdot b+ a\cdot c[/tex]
We know that
[tex]i^2= -1[/tex] where i is the imaginary
Given the complex numbers:
A.
[tex]i^2(2i^2-5)[/tex]
⇒[tex]-1(2(-1)-5) = -1(-2-5)= -1(-7) = 7[/tex]
B.
[tex]i^2(3+i^2)[/tex]
⇒[tex]-1(3+(-1)) = -1(3-1)= -1(2) = -2[/tex]
C.
[tex]2i(2i-i^3)[/tex]
Using distributive property
⇒[tex]4i^2-2i^4[/tex]
⇒[tex]4(-1)-2(i^2)^2 = -4-2(-1)^2 = -4 -2 = -6[/tex]
D.
[tex]i(4i^3-i)[/tex]
Using distributive property
⇒[tex]4i^4-i^2[/tex]
⇒[tex]4(i^2)^2-i^2[/tex]
⇒[tex]4(-1)^2-(-1) = 4+1 = 5[/tex]
Therefore. matching defined as:
A. [tex]i^2(2i^2-5)[/tex] → 7
B. [tex]i^2(3+i^2)[/tex] → -2
C. [tex]2i(2i-i^3)[/tex] → -6
D. [tex]i(4i^3-i)[/tex] → 5
