In Exercises 61–64, write each complex number in standard form.

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Question

In Exercises 61–64, write each complex number in standard form.

(1 - i)^3

Accepted Answer

Welcome back. I'm so glad you're here. We've got this expression to minus I all cubed more to write it in standard form. Well what is standard form? We've got that I meaning that we're dealing with complex numbers here. In the standard form for complex numbers is A plus B. I. And it's really close. It's almost in standard form except it's cute and it'd be great if we could just take that three and distribute it. But that is a common mistake and we cannot do that. We've got to rewrite it as we've got two minus I times two minus I times two minus I. And now we can just go ahead and start foiling that out. Looking at these first two here two times two is four And our outsides two times negative I is -2. I our insides negative I times two is again -2. I and our last negative I times negative. I well that's going to be plus I squared. And bring the rest down parentheses and two minus I. Now let's combine like terms negative two I minus two. I will give us four minus four. I plus I squared all times two minus I. But hang on a second we recall from previous lessons that I squared. Well that means something we know that I to the first equals I that I squared equals negative one eye to the third equals negative I and I to the fourth equals positive one so that I squared right there is a negative one. So it's four minus four I minus one. All times two minus I And again we can combine like terms here, four minus one is three. So we've got three minus four I times two minus I. And look at that we can just start foiling again three times two is six. Our Outsides three times negative eyes negative three. I our insides negative four times two is negative eight. I and our last negative four I times negative I that's going to be a positive for I squared and don't forget to square that again, let's combine like terms and while we're at it we know that that I squared is going to be negative one. So six we have negative three I minus eight. I will give us minus 11 I and plus four I squared. Well that's four times negative one. Or just negative four. And again we can combine like terms six minus four, that is two. So we have two minus 11. I we can't combine those and that is in our standard form. So we look at our answer choices and that matches with answer choice. A That whole thing was a bit more complex than it looked on the surface. Huh? That was a bad joke. But anyway, well done. We'll catch you on the next one

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