Question

Factor 4x^2+81 over the set of complex numbers

Answer 1

Answer:(2x + 9i)(2x - 9i)

Explanation:

a^2 - b^2 = (a+b)(a-b)

a^2 + b^2 = (a+bi)(a-bi) = a^2 + abi - abi - b^2 i^2

But -b^2 i^2 = +b^2

Answer 2

`(4x+9i)(4x-9i)`

Explanation:

Here, we have to apply this complex numbers property:

`a^2 + b^2 = (a+bi)(a-bi)`

So, the given expression
`4x^2+81`, can be rewrite as factor using the property:

`4x^2+81=(4x+9i)(4x-9i)`

Because, if

`a^2=x^2 \ and \ b^2=81\\\ then \ a=x \ and \ b=9`

Therefore, the factors are
`(4x+9i)(4x-9i)`