Question

complex numbers online practice
complete this assessment to review what youve learned. it will not count toward yo
what is the product of the multiplication $(5 - 3i)(-2 + 6i)$? (1 point)
\\(\circ -10 + 18i\\)
\\(\circ -28 + 36i\\)
\\(\circ 8 + 36i\\)
\\(\circ -10 - 18i\\)

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first complex number by each term in the second:
$(5 - 3i)(-2 + 6i) = 5(-2) + 5(6i) - 3i(-2) - 3i(6i)$

Step2: Simplify each term

• $5(-2) = -10$
• $5(6i) = 30i$
• $-3i(-2) = 6i$
• $-3i(6i) = -18i^2$ (and $i^2 = -1$, so $-18i^2 = 18$)

Step3: Combine like terms

Combine real parts and imaginary parts:
Real: $-10 + 18 = 8$
Imaginary: $30i + 6i = 36i$

Answer:

$8 + 36i$ (corresponding to the option "8 + 36i")