In Exercises 9–20, find each product and write the result in stan...

Question

In Exercises 9–20, find each product and write the result in standard form.

(3 + 5i)(3 - 5i)

Accepted Answer

Hello. Everyone in this video we're going to be working on this practice problem where we're dealing with complex numbers and we want to express our answer in standard form and the multiplication that we're going to be doing is 1 -1 times one plus I. So whenever you're multiplying complex numbers, it's very similar to multiplying polynomial is where you want to multiply every single term in the first parentheses to every single term in the second set of parentheses. So in this case if we do one times one we're left with one then one times positive. I is positive. I and then we have negative I times one is negative I and the negative I times positive I is negative I squared. And you can see that these middle terms cancel each other out. So I'm going to write those as zero and I'm left with one minus I squared. So when you're dealing with complex numbers it's also important to remember that i is equal to the square root of negative one. So I squared is equal to negative one. So using this I'm going to go back to my expression and wherever I see I squared, I'm going to replace with negative one. And if I do that I'm left with one minus parentheses negative one. And if I solve that it's one plus one which leaves me with two and you can see that there's no more imaginary components in my answer. But that's because they canceled L. So this becomes my final answer and this aligns with answer choice C. My final answer is two. So hopefully this video helped and see you next time.

In Exercises 9–20, find each product and write the result in standard form. (3 + 5i)(3 - 5i)

Key Concepts

Complex Numbers

Multiplication of Complex Numbers

Standard Form of Complex Numbers

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