Question

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perform the indicated operation & simplify. express the answer as a complex number.
$(10 + \sqrt{-144})(-6 + \sqrt{-121})=$ enter your answer
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Explanation:

Step1: Simplify square - roots of negative numbers

Recall that $\sqrt{-a}=i\sqrt{a}$ for $a>0$. So, $\sqrt{-144} = 12i$ and $\sqrt{-121}=11i$.
The expression becomes $(10 + 12i)(-6+11i)$.

Step2: Use the FOIL method

$(10 + 12i)(-6+11i)=10\times(-6)+10\times11i+12i\times(-6)+12i\times11i$.
$=-60 + 110i-72i+132i^{2}$.

Step3: Substitute $i^{2}=-1$

Since $i^{2}=-1$, we have $-60 + 110i-72i+132\times(-1)$.
$=-60 + 110i-72i-132$.

Step4: Combine like - terms

Combine the real parts and the imaginary parts: $(-60-132)+(110i - 72i)$.
$=-192 + 38i$.

Answer:

$-192 + 38i$