five The complex numbers for I divided by three plus I. Now, in order to do that, we're going to the college you get of the complex number so we're gonna multiply the denominator so they're gonna multiply by three minus I on both the numerator and the denominator. So that's when I do distributive property for the numerator is that's gonna be 12. I minus four. I squared and we'll simplify that in the morning minute for the denominators we're gonna use full. Our first terms would be three times three is nine are outside. Terms would be negative. Three i and three I and those were actually gonna cancel out in our last terms would be negative. I square. So we know that negative. I squared. So let's reduce that. That would be non minus. I squared. Well, in both of these cases, we know that I squared is negative one. So let's replace our I squares with negative one. So that's 12 I, minus four times negative. One over nine minus negative one. So what we've got now is 12. I plus four over. That's gonna change the nine plus one, which would be 10. So we can simplify that more. Let's do our numbers that do not that are not the complex numbers. So let's do the 4/10 plus 12/10 I. And let's reduce our fractions. 4/10 is going to reduce to 2/5 and 12/10 is gonna reduce to 6/5 I. So our solution is to fist plus six fists I

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five The complex numbers for I divided by three plus I. Now, in order to do that, we're going to the college you get of the complex number so we're gonna multiply the denominator so they're gonna multiply by three minus I on both the numerator and the denominator. So that's when I do distributive property for the numerator is that's gonna be 12. I minus four. I squared and we'll simplify that in the morning minute for the denominators we're gonna use full. Our first terms would be three times three is nine are outside. Terms would be negative. Three i and three I and those were actually gonna cancel out in our last terms would be negative. I square. So we know that negative. I squared. So let's reduce that. That would be non minus. I squared. Well, in both of these cases, we know that I squared is negative one. So let's replace our I squares with negative one. So that's 12 I, minus four times negative. One over nine minus negative one. So what we've got now is 12. I plus four over. That's gonna change the nine plus one, which would be 10. So we can simplify that more. Let's do our numbers that do not that are not the complex numbers. So let's do the 4/10 plus 12/10 I. And let's reduce our fractions. 4/10 is going to reduce to 2/5 and 12/10 is gonna reduce to 6/5 I. So our solution is to fist plus six fists I

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