Question

multiply: $(4 + 5i)(3 - 2i)$.\
\
a. $-22 - 7i$\
\
b. $22 + 7i$\
\
c. $-22 + 7i$\
\
d. $22 - 7i$

Explanation:

Step1: Apply distributive property (FOIL)

$(4+5i)(3-2i) = 4\times3 + 4\times(-2i) + 5i\times3 + 5i\times(-2i)$

Step2: Calculate each term

$= 12 - 8i + 15i - 10i^2$

Step3: Substitute $i^2=-1$

$= 12 - 8i + 15i - 10\times(-1)$

Step4: Simplify real and imaginary parts

$= 12 + 10 + (-8i + 15i) = 22 + 7i$

Answer:

B. $22 + 7i$