Question

Match each product of complex numbers with its value.

Pairs -6, 5 , 7 , -2
complex numbers i^2(2i^2-5) , i^2(3+ i^2) , 2i(2i- i^3) , i(4i^3-i)

Answer 1

`i^2(2i^2-5) \rightarrow 7`

`i^2(3+i^2) \rightarrow -2`

`2i(2i-i^3) \rightarrow -6`

`i(4i^3-i) \rightarrow 5`

Answer 2

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