Question

multiply. choose the correct answer from the choices below.
$(5 - i)(-3 + 2i)$
a $-13 + 7i$
b $-13 + 13i$
c $-17 + 7i$
d $-17 + 13i$

Explanation:

Step1: Use distributive property (FOIL)

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

Step2: Simplify each product

Calculate each product:
$$5\times(-3)= -15$$
$$5\times(2i)=10i$$
$$-i\times(-3)=3i$$
$$-i\times(2i)= -2i^{2}$$
Recall that \(i^{2}=-1\), so \(-2i^{2}=-2\times(-1) = 2\).

Step3: Combine like terms

Combine the real parts and the imaginary parts:
Real parts: \(-15 + 2=-13\)
Imaginary parts: \(10i+3i = 13i\)
So, \((5 - i)(-3 + 2i)=-13 + 13i\)

Answer:

B. \(-13 + 13i\)