Question

current learning objective: multiplying complex numbers
question 8
score: 0 of 1 point
perform the indicated operation & simplify. express the answer as a complex number.
(5 + √(-1))(-6 + √(-81)) = enter your answer
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Explanation:

Step1: Recall the definition of imaginary unit

Recall that $\sqrt{-1}=i$ and $\sqrt{-81}=\sqrt{81}\times\sqrt{-1}=9i$.
So the expression becomes $(5 + i)(-6+9i)$.

Step2: Use FOIL method

$(5 + i)(-6+9i)=5\times(-6)+5\times9i+i\times(-6)+i\times9i$.
$=-30 + 45i-6i+9i^{2}$.

Step3: Simplify using $i^{2}=-1$

Since $i^{2}=-1$, we have $-30 + 45i-6i+9\times(-1)$.
$=-30-9+(45i - 6i)$.
$=-39 + 39i$.

Answer:

$-39 + 39i$