Question

simplify the expression (3 - 4i)(5 + 2i)

Explanation:

Step1: Apply FOIL method

$(3-4i)(5+2i) = 3\times5 + 3\times2i -4i\times5 -4i\times2i$

Step2: Calculate each term

$= 15 + 6i -20i -8i^2$

Step3: Substitute $i^2=-1$

$= 15 + 6i -20i -8\times(-1)$

Step4: Simplify real and imaginary parts

$= 15+8 + (6i-20i)$
$= 23 -14i$

Answer:

$23 - 14i$