Respuesta :

Option C:

The product of 3 - 4i and -6 + i is -14 + 27i.

Solution:

Given complex numbers are 3 - 4i and -6 + i.

To find the product of these numbers.

Product of 3 - 4i and -6 + i

            [tex]=(3 - 4i)(-6 + i)[/tex]

Multiply each term of first number with each term of second number.

            [tex]=3 (-6 + i)-4i(-6+i)[/tex]  

            [tex]=3 (-6) + 3i -4i (-6)-4i^2[/tex]

Since the value of i² = -1

            [tex]=-18+ 3i +24i-4(-1)[/tex]

            [tex]=-18+27i+4[/tex]

            [tex]=-14+27i[/tex]

The product of 3 - 4i and -6 + i is -14 + 27i.

Option C is the correct answer.

facundo3141592

Here we just want to find the product of two complex numbers, we will see that the solution is -14 + 27i

Remember that the complex number i has the property:

i^2 = -1

Now we want to perform the multiplication between 3 - 4i and -6 + i

Then we have:

(3 - 4i)*(-6 + i) = -18 + 3i + (4i)*6 - (4i)*i = -18 + 27i + 4 = -14 + 27i

So the correct option is C.

If you want to learn more about complex numbers, you can read:

https://brainly.com/question/10662770

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