evaluate $(5 - 2i)(-3 + 7i)$ if $i$ is the imaginary unit.$-19 + 41i$$-1 + 41i$$-1 + 29i$$19 + 29i$
evaluate $(5 - 2i)(-3 + 7i)$ if $i$ is the imaginary unit.$-19 + 41i$$-1 + 41i$$-1 + 29i$$19 + 29i$
Answer
Explanation:
Step1: Apply FOIL method
$(5-2i)(-3+7i) = 5(-3) + 5(7i) + (-2i)(-3) + (-2i)(7i)$
Step2: Calculate each term
$= -15 + 35i + 6i - 14i^2$
Step3: Substitute $i^2=-1$
$= -15 + 35i + 6i - 14(-1)$
Step4: Simplify real terms
$= -15 + 14 + 35i + 6i$
Step5: Combine like terms
$= -1 + 41i$
Answer:
$-1 + 41i$