Question

Multiply: (–4 + i)(2 – 3i)

Question 8 options:

–8 + 11i


–5 + 14i


–11 + 14i


–5 – 10i

Answer 1

To multiply the complex numbers (–4 + i) and (2 – 3i), we use the distributive property to find –5 + 14i as the result.

Step-by-step explanation:

It is asked to multiply the complex numbers (–4 + i) and (2 – 3i). To multiply these two complex expressions, we use the distributive property (also known as the Foil method in this context) to multiply each term in the first expression by each term in the second expression.

The multiplication is carried out as follows:

• (–4) × (2) = –8
• (–4) × (–3i) = +12i
• (i) × (2) = +2i
• (i) × (–3i) = –3i²

Since i² = –1, the last term becomes –3(–1) = +3. Combining like terms, we have:

–8 + 12i + 2i + 3 = (–8 + 3) + (12i + 2i) = –5 + 14i

Therefore, the product of the two complex numbers (–4 + i) and (2 – 3i) is –5 + 14i.

Answer 2

B

Step-by-step explanation:

-4*2=-8

-4*-3i=12i

i*2=2i

i*-3i=3

-8+3=-5

12i+2i=14i

-5+14i