in-26-37-find-each-product-leftfrac15-frac110-iright42-i

Question

In $26-37,$ find each product.
$$
\left(\frac{1}{5}-\frac{1}{10} i\right)(4+2 i)
$$

Jeremy Strong · Accepted Answer

in this problem. We&#x27;re asked most by the complex number 1/5 Modest. 1/10 of the complex number four plus two. Uh, so we will perform multiplication as usual, using the foil method. So to begin, we have 1/5 Tom&#x27;s four, which is going to give us four. It&#x27;s okay. And then our outer terms are we have 1/5 and we have to Ah, multiplying this together is going to get us to fifths, huh? And then our inner terms, we have modest 1/10 I and we have four. Multiplying them is going to give us modest four chance high in our last terms. Won&#x27;t negative 1/10 and positive to our We&#x27;re gonna give us a modernist to over 10 uh, squared. Now I squared is the same thing is negative one because it is the square root of negative one squared. So we have modest to chance times negative one. So, actually, what we can do here is we can forget. The negative one is here and make the 2/10 positive. Now we need to combine our real parts and our imaginary parts. So we have 4/5 and we have plus two chance. So 4/5 is the same thing is a chance. And then we have plus to chance for a real component. And then we have 2/5 Monas for Fitze has shown here. So what we could do is we could rewrite to Fitz a cz four over 10. Uh and then we have Monness 40 Virgin, huh? So for our real component, we have 8/10 plus two chance, which is Jan over 10. And then for our imaginary component, we have four chance. Ah, modest fortune saw, which is zero I and 10 over 10. Plus Cyril, I may be rewritten as simply one, which is final answer.

Jeremy Strong · Answer

for this problem were asked by the complex number one plus fava by the complex number one plus two. So to do this we may use the foil method. So we 1st 1 won&#x27;t spot one times one to get one and then we multiply the outer terms the two I and the one which will give us a plus two. Uh And then we will multiply the inner terms five and one to give us a plus five I And then we were multiple. The last terms which will be the five and the two I to give us plus 10 squared. Now if we attempt to add correspondent components, we have one and then we have a two and a father which combining with seven and then we have plus 10 times square. Now I squared is the square root of negative one squared, which is actually negative one. And this works out to be one mon ist tim plus seven I, which is equal to negative non plus seminar and negative non plus seven. Ah, is the final answer

Heather Zimmers · Answer

to multiply complex numbers. We use the same technique we would use to multiply by no meals, and that would be the foil method. So we multiply the first and we get 12. We multiplied the outside&#x27;s when we get negative. Eight. I we multiply the insides and we get negative. 15 I and we multiply the last and we get plus 10. I squared. Now let&#x27;s combine like terms. Negative eight I and negative 15 I and we have 12 minus 23 I and remember that I squared is negative one. So we have plus 10 times negative one. So if we simplify that, we have 12 minus 23 I minus 10. And let&#x27;s go ahead and add those like terms together, and our final answer will be to minus 23 I

Heather Zimmers · Answer

to multiply complex numbers. We use the same method we would use if we were multiplying by no meals. And that would be the foil method. So we multiply the first and we get negative, too. Welcome by the outsides, and we get negative. Four. I multiply the insides and we get negative one I and multiply the last time we get negative to I squared. Let&#x27;s combine the inside and outside terms so we have negative two minus five I and then remember that I squared is negative one. So we have minus two times negative one. So we&#x27;ll simplify that. We have negative two minus five I plus two and we can add the negative to in the plus two and they just give us zero. So in standard form we have zero minus five I

Heather Zimmers · Answer

to multiply complex numbers. We can use the same method we would use to multiply by no meals, which would be the foil method. And we could just jump right in and start using the foil method now. But I&#x27;m going to be a little bit more strategic than that. I&#x27;m going to take a look at the second factor and noticed that we could factor 1/10 out of both terms. So I&#x27;m going to think of this as three minus I times three plus high times 1/10 and I&#x27;m going to start by multiplying the three plus I in the three minus side together. So using the foil method, we have three times 39 for the 1st 3 times I for the outside three i For the inside, we have negative three I and for the last we have minus I squared and that is still all multiplied by 1/10. So let&#x27;s take a look at that. We have a positive three I and a negative three I those at 20 And don&#x27;t forget that I squared equals negative one. So we have nine minus negative one times 1/10. Well, that&#x27;s the same as 10 times 1/10. So the answer is one

Jeremy Strong · Answer

in this problem, we arrest most by the complex number five Modest three out by the complex number five plus three to begin. You may notice that these two complex numbers are complex contra hits. But for now, we will ignore this and we will continue the multiplication as we normally would. So to begin, we have to foil this expression. So we have five times, which is gonna give us 20 five. Our outer components are plus three and plus five, which is gonna give us plus 15. I, our inner components are modest area and positive five to give us monos 15 I and our outer components are modest. Three out and positive three out to give us modest non, uh, squared. Now Ah, squared is a very negative one squared. So this actually one to cancel to give us a negative one. Now, since we have a mon isn on multiple about modest one, this term will cancel out to go. It&#x27;s a plus. None. Now we have 25 plus nine to give us 34 and then we have plus 15 out modest 59 which is going to give us plus zero I and that is going to give us a final answer of simply 34. Now it is worth mentioning that when you multiply complex number by its complex congregate, there actually is a simple formula for doing so. The formula is a squared plus B squared where a it&#x27;s the real component and B is the imaginary component. In this case, a equaled five equals five and B equals three. So by the formula, our answer should be of squared plus three squared, which is equal to 25 plus nine, which is going to give us 34 which is the answer we got.

Problem

In $26-37,$ find each product. $$ \left(-\frac{…

Problem 36 Medium Difficulty

In $26-37,$ find each product.
$$
\left(\frac{1}{5}-\frac{1}{10} i\right)(4+2 i)
$$

Answer

1

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