Find each quotient. Write answers in standard form. 2-i / 2+i

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Accepted Answer

Hello everyone. We're going to divide the expression 21 -1 divided by plus. I First thing I'm gonna do is rewrite this as a fraction. So I have 21 minus I over 21 plus. I I recall that in math we don't want imaginary numbers in the denominator and that I need to multiply top and bottom by something to get rid of it. In this case we're going to use what we call a conjugate which is the same terms as our denominator but with the opposite sign in between. So here we have 21 -1 as our conjugate Noticing that 21 -1 times 21 -1 is what I have in my numerator I can treat this as if it was a square. So when I do that I square. The first term 21 squared is square. The last term I squared. And then for the middle term I take the product of the two terms and double it so negative I times 21 is negative. 21 I doubled is negative 42. I in my denominator congregates are chosen specifically to give us a situation where we have the difference of squares. This means our middle terms cancel out so we can square. The first term 21 squared is again square. The last term I squared and put a minus sign in between them Recalling that I squared is the same as -1. I'm going to replace I squared with negative one every time it shows up. So 441 -42. I plus negative one over -30. Now I'm gonna clean up my like terms and see what we have In the numerator. My like terms are 441 and -1. So those can combine to 440 -42. I In my denominator double negatives are like adding. So 441 plus one is 442 and we're almost done but we're not quite there yet because we're not in standard form yet. To get this into standard form, I need to split it into two fractions Until I get 440 Over -40 to over 442. And the I can be at the tail end of this fraction. So one last step I want to reduce these fractions if I can Now if nothing else I know they can be reduced by two and that's where I'm going to start. So 440, divided by two is 220. 442 divided by two is 221. In my second fraction again I think two is my best choice, 42, divided by two is 21. 442 divided by two is 221 and the I can hang at the back of this fraction. So our solution is over 221 -21 over i. And that would be in standard form because the real part comes before the imaginary part, and it is answer choice B. Have a nice day.

Find each quotient. Write answers in standard form. 2-i / 2+i

Key Concepts

Complex Numbers

Division of Complex Numbers

Standard Form of Complex Numbers

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