Questions: Factor 16 x^2+121 over the set of complex numbers.

Transcript text: Factor $16 x^{2}+121$ over the set of complex numbers.

Solution

Solution Steps

Step 1: Recognize the form of the expression

The given expression is $16x^{2} + 121$. This is a sum of squares, which can be factored over the complex numbers using the formula $a^{2} + b^{2} = (a + bi)(a - bi)$, where $i$ is the imaginary unit.

Step 2: Rewrite the expression as a sum of squares

Rewrite $16x^{2}$ and $121$ as perfect squares: \[ 16x^{2} = (4x)^{2}, \quad 121 = 11^{2}. \] Thus, the expression becomes: \[ (4x)^{2} + 11^{2}. \]

Step 3: Apply the sum of squares formula

Using the formula $a^{2} + b^{2} = (a + bi)(a - bi)$, substitute $a = 4x$ and $b = 11$: \[ (4x)^{2} + 11^{2} = (4x + 11i)(4x - 11i). \]

The expression is now factored over the complex numbers.

Final Answer

$\boxed{(4x + 11i)(4x - 11i)}$

Was this solution helpful?

Unhelpful

Helpful

Next >

Questions: Factor 16 x^2+121 over the set of complex numbers.

Solution

Solution Steps

Final Answer

Questions asked by other users