Find each quotient. Write answers in standard form. 1-3i / 1+i

Question

Accepted Answer

Hello everyone. We're going to divide the expression 14 -4. I divided by seven plus I. First thing I'm gonna do is rewrite it as a fraction. So 14 -4 I is my numerator seven plus I is my denominator. In math. We don't want to have an imaginary number in the denominator. So we need to multiply top and bottom by a factor of one to get rid of that. Since our denominator is a binomial we're gonna use what we call a conjugate which means it has the same terms as the denominator but with the opposite sign. So in this example the conjugate is 7 -1. And now I'm gonna multiply this through like I did any other binomial. So I'm gonna use foil. First is 14 times seven which is 98. Outer 14 times negative I which is negative 14 I in er negative four I times seven which is negative 28 I and last negative four I times negative I which gives me a plus four I squared for the denominator. We picked our conjugate on purpose to run into the situation of difference of squares. This means we square a first term. So seven squared is 49 square. Last term I squared is I squared to minus in between recall that when we have an I squared it's the same as negative one. So I'm going to substitute that in so minus 14 I minus I plus four times negative one. And in the Denominator 49 -20. So in this next step I'm going to combine my like terms. So in the name, Raider, stays 98, -14, I -28. I gives me -42 I four times negative one gives me a negative four. In my denominator double negatives are like adding. So this is like 49 plus one. So 50 And then I have one more set of like terms I can combine in my numerator now that I've multiplied in my negative one. So 98 -4 is -42. I over 50. Now we're almost done but we want this in standard form. So that means we're going to split this into two fractions the real number section. So 94/50 minus the imaginary section. So 42 I over And one last thing we want to reduce our fractions. So looks like the largest thing I can reduce. The first fraction by is by two. So 94 divided by two is 47, 50, divided by two is 25. In my second fraction Again it looks like two is the best thing to reduce by. So I get 42 divided by two is And 50 divided by two is 25. So we end up with the solution of 47/ -21/25. I this is our solution and that is answer choice. C have a nice day

Find each quotient. Write answers in standard form. 1-3i / 1+i

Key Concepts

Complex Numbers

Division of Complex Numbers

Standard Form of Complex Numbers

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