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Find the product of 2 4i and its conjugate. The answer is a + bi whereThe real number a equalsThe real number b equals...

Question

Find the product of 2 4i and its conjugate. The answer is a + bi whereThe real number a equalsThe real number b equals

Find the product of 2 4i and its conjugate. The answer is a + bi where The real number a equals The real number b equals



Answers

Find the product of the given complex number and its conjugate.
$$ 2+6 i $$

Okay, were given the complex number four minus six I. So it's congregate would be four plus six. I they have opposite signs Contra gets do so we're gonna multiply these together. You just treat I like it's a variable and treat this like you were multiplying by no meals. So we're gonna use the foil process. So we multiply the first and we get 16. Multiply the outsides and we get 24. I multiply the insides and we get minus 24 I and multiply the last thing we get minus 36. I squared so we can combine the light terms 24 i and minus 24 I and those ad to zero. So now we have 16. Minus 36. I squared. Remember that I squared is defined his negative one. So every time you get in, I squared. You're going to replace it with a negative one. So we have 16 minus 36 times. Negative one, and that would be 16 plus 36. And that's 52

Okay, were given the complex number negative two plus I so it's congregate would be negative to minus I They have opposite signs in the middle. And so now we're gonna multiply these together. And when you multiply complex numbers, you just treat I like you would a variable and you could multiply this like you would foil. So if we multiply the first, you get negative or you get positive for multiply the outsides and you get positive to I multiply the insides and you get minus two eye and multiply the last and you get minus. I squared. Now you can add together the two I and the negative to I and those and a zero. So now we have four minus. I squared And don't forget that I squared is defined his negative one. So every time you get in, I squared. You're going to replace it with negative one. So now we have four minus negative one, and that's four plus one. So we have five

Okay, were given the complex number Square root five minus four I. So it's congregate would be square root. Five plus four. I won with a plus one with a minus those air con tickets. And now we're gonna multiply them together. So you just treat. I like you would a variable, and we're going to multiply this like we would foil. So multiply the first and we have square root five times square root five, which is five. Multiply the outsides and we have four square root five I well, the planet insides and we have minus for square root five i and multiply the last and we have minus 16. I squared looking at the middle two terms plus four square root five I minus four square root five I those would add to zero. So what we have left is five minus 16. I squared and remember that I squared is to find his negative one. So every time you get I square, you're going to replace it with negative one. So now we have five minus 16 times negative one, which is five plus 16. So our answer is 21

Okay, so we want to multiply to falling number where it's calling you get. So let's get a four. What? Seven. I So it's recall. That's if we have a plus B I and we multiply it by a minus. Bi I Elliott's This is the difference of squares. Do we get a squared? And then we have minus He's way. Okay, so just give just a, um, figure four squared minus seven. I What? So we get, um actually what? Some? Which I could so yet a squared minus B. I must be I. And then we have minus B squared times. I squared. So this gives us a squared plus b squared. So this gives us, um, a score in tonight's thinking of four squared plus B squared, which is okay, a seven. So we get seventh word. So that's going to be 16 plus 49 and I would 16. Close 49. This gives us a 65


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