QuestionFactor the expression $121 r^{2}+4 s^{2}$ in the complex number set.

Studdy Solution

STEP 1

Assumptions1. We are factoring the expression over the set of complex numbers. . The expression to be factored is 121r^ +4s^.

STEP 2

The expression $121r^2 +4s^2$ is a sum of squares, which can be factored using the formula $a^2 + b^2 = (a + ib)(a - ib)$ , where $i$ is the imaginary unit.

STEP 3

In our case, $a$ is $11r$ and $b$ is $2s$ . This is because $121r^2 = (11r)^2$ and $s^2 = (2s)^2$ .

STEP 4

Substitute $11r$ for $a$ and $2s$ for $b$ in the formula $a^2 + b^2 = (a + ib)(a - ib)$ .
$121r^2 +4s^2 = (11r +2si)(11r -2si)$

STEP 5

So, the factored form of the expression $121r^2 +4s^2$ over the set of complex numbers is $(11r +2si)(11r -2si)$ .
The factored expression is $(11r +2si)(11r -2si)$ .

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