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.

(2 + 3i)^2

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we're dealing with multiplying complex numbers and we want to make sure that our answer is expressed in Standard form. And the multiplication that we're going to be doing is to I -1 squared. So if I write this out I have to I -1 times two I -1. So when you're multiplying complex numbers, it's very much like multiplying polynomial where you want to multiply each term to the terms in the second parentheses. Or you can follow the foil method where you multiply the first terms together than the outer terms together and then the innermost and the last terms of each parentheses. So if we carry out those multiplication, the first terms to I times two I then we have the Outer terms. So two i times negative one. And then we have the inner terms negative one times two. I. Is And then the last terms negative one times negative one. So now we can complete these multiplication. So two I times two I is for I squared and then we have negative one times two. I so minus two. I and again we have negative one times two. I so minus two. I. And then we have negative one times negative one. So positive one. And we can combine these two middle terms. So we're left with four I squared minus four I plus one. So when you're dealing with complex numbers it's also important to remember that I represents the square root of negative one. So if we have I squared that is negative one. So I'm going to go back into my equation and wherever I see I squared, I'm going to replace it with negative one. So I have four I squared. So I'm gonna change that to four times negative one minus four I plus one. So if I do that multiplication, I have negative four plus one minus four. I notice how I just moved this one over to the left to make sure that all my real components were together. So now I have negative four plus one. That leaves me with negative three minus four. I So this is already in standard form because I have the real part in first and then the imaginary part. Remember standard form is real plus the imaginary part. So this becomes my final answer for this multiplication. And you can see that this aligns with answer choice a negative 3 -4. I so hopefully this video helped and see you next time.

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