Question

Find the following product and write the result in standard form, a + bi. (-6+i)(3+i) (-6+i)(3+i)

Answer 1

The product of the complex numbers (-6+i) and (3+i) is calculated using the distributive property and results in -19 - 3i when written in standard form.

Step-by-step explanation:

To find the product of two complex numbers and write the result in standard form a + bi, we will use the distributive property (also known as FOIL in the context of binomials) to multiply (-6+i) and (3+i).

First, we multiply the real parts: -6 × 3 = -18.
Next, we multiply the real part of the first number by the imaginary part of the second: -6 × i = -6i.
Then, we multiply the imaginary part of the first number by the real part of the second: i × 3 = 3i.
Finally, we multiply the imaginary parts: i × i = i² = -1 (since i² = -1).

Now, we combine the results: -18 + (-6i) + 3i - 1.
Simplifying the imaginary parts: -6i + 3i = -3i.
Combining real parts: -18 - 1 = -19.

The product in standard form is: -19 - 3i.