Find each product and write the result in standard form. (- 5 ...

Question

Find each product and write the result in standard form. (- 5 + i)(- 5 - i)

Accepted Answer

Hello everyone in this video. We're gonna be looking at this problem where we have complex numbers and we want to make sure that our answers expressed in standard form. So we're going to be finding the product between I -3 times negative I -3. So whenever you're multiplying complex numbers it's very similar to multiplying polynomial. Where you want to multiply every single component in the first parentheses to every single component in the second parentheses. So if we do that we have I times negative I is negative I squared, then I times negative three is negative three. I. And then we have negative three times negative. I we get positive three I And the - times negative three is positive nine. So now I have multiplied every single component from the first parentheses to every single component in the second parentheses. And you can see that these middle terms cancel out so that is zero and we're left with negative I squared Plus nine. And whenever you have complex numbers it's important to remember that I is equal to the square root of negative one So I squared is equal to negative one. So I'm gonna go back to my expression here and wherever I see an I squared I'm gonna replace it with negative one. If I do that I'm left with negative negative one because I replaced the I squared plus nine. So this becomes one plus nine and that is 10. So this is my final answer. As you can see there's no imaginary component since they canceled out. And that aligns with answer choice D. So hopefully this video helped and see you next time.

Find each product and write the result in standard form. (- 5 + i)(- 5 - i)

Key Concepts

Complex Numbers

Multiplication of Complex Numbers

Standard Form of a Complex Number

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