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