Question

Multiply two complex numbers :

(-4-8i)(3+i)

Answer 1

To multiply the complex numbers (-4-8i) and (3+i), we follow the distributive property, combining like terms after multiplying each pair of terms, resulting in a final product of -4 - 28i.

Step-by-step explanation:

To multiply two complex numbers such as (-4-8i)(3+i), we apply the distributive property (also known as the FOIL method in this context — which stands for First, Outer, Inner, Last). Here's the step-by-step calculation:

1. Multiply the First terms: (-4) × 3 = -12.
2. Multiply the Outer terms: (-4) × i = -4i.
3. Multiply the Inner terms: (-8i) × 3 = -24i.
4. Multiply the Last terms: (-8i) × i = -8i². Since i² = -1, this is equivalent to 8.

Combine these results: -12 - 4i - 24i + 8.

Combine like terms (the real numbers and the imaginary numbers separately): (-12 + 8) + (-4i - 24i).

Simplify the expression: -4 - 28i.

The product of the given complex numbers is -4 - 28i.