ethan-said-that-the-square-of-any-pure-imaginary-number-is-a-negative-real-number-do-you-agree-with-

Name: ethan said that the square of any pure imaginary number is a negative real number do you agree with
Uploaded: 2019-07-31
Duration: 1 min 32 s
Channel: Numerade
Description: Ethan said that the square of any pure imaginary number is a negative real number. Do you agree with Ethan? Justify your answer.

Question

Ethan said that the square of any pure imaginary number is a negative real number. Do you agree with Ethan? Justify your answer.

Martha Richards · Accepted Answer

Okay, So what this question is asking is is if you take any pure imaginary number and you square it well, that turned out to be a negative riel number. And so basically, we could do a couple of examples. We know that a pure imaginary number is some really number, eh? That&#x27;s not zero times this eye here. And so let&#x27;s do a couple of examples. If I said okay, well, what about five? I if I squared that well, what would that be? That would be we&#x27;ve got to distribute this, too. So that would be five squared, And that would be I squared. And we know that I squared is a negative one and five square goes to 25. And so this would be a negative 25. So in this particular case, it does seem true that this would become a negative real number. But let&#x27;s try another number. Let&#x27;s try another pure imaginary number. What if I had a negative five? I So here, if we square this again, we&#x27;re gonna square. We&#x27;re going to distribute that to, and I&#x27;m going to get a negative five squared and I&#x27;m hit again. Haven&#x27;t I squared And that&#x27;s going to be This goes to a negative one this year and negative times and negative is a positive. So this is goes to 25 we&#x27;re back again to a negative rial number. So I guess we&#x27;re going to agree with Ethan on this one.

Jeremy Strong · Answer

in this problem, Joshua claims Prada a complex number, and it&#x27;s conjugated is always a real number. And we know that any complex number can be expressed in the form A plus B A. So we have a plus be, huh? And the complex conjugated is just going to be the reverse of the imaginary component. So it&#x27;s going to be a modest BIA. And when we multiply these two things together, we&#x27;re going to use the foil method or we can use the distributive property twice. But when we do this, we&#x27;re going to get a squared monness a B ah, plus A B uh Monness B squared, squared. Now we know that negative Abia and positive AP are going to cancel one another out. Now we have a monitor B squared Oscar. Well, I squared is the spirit of negative one squared, which is a negative one. So we actually have a squared plus B squared, which is always going to be a real number because there is no imaginary component left after we perform the multiplication

M S · Answer

So Jennifer said that the fourth Roots, uh, a squared is the square root of a Do we disagree or agree? I agree, and I&#x27;ll show you what. So whenever you have the square root of a number will stay. In this case, there&#x27;s always been understood to here, and everything has an explanation. Boy. Already. So we want to write this with the fractional exponents will have a to the wood half. So another way to write our left hand side would have before three to base. We&#x27;re no other way to write this with Braxton. Explain it will have a report. Did you tell you the number under the house and put it over the number outside of the house. And to reduce that fraction, we&#x27;ll have a to the 1/2. And to rewrite that with a square root will help the square root of a and it is our right hand side. So we I agree

Jeyasree R T · Answer

Yes, it is possible. Disquieting. Imagining the world. Get a your number. Yes, for example. Consider think imaginary number. We know that the value off ice choir this in this one, which is you remember so And situs? Yes.

Julie Silva · Answer

So this problem. We&#x27;re told that the student, Emily, said that when A and C are real numbers with same sign and B equals zero, the roots of the equation a X squared plus BX plus C equals zero are pure imaginary. Do we agree? And then we want to justify our answer. Well, if B is zero and and see have the same sign, let&#x27;s think about what would happen when we use our quadratic or formula. So let&#x27;s say a was equal to two and C was equal to, I don&#x27;t know. So they wrote the same sign. They&#x27;re both positive and again she&#x27;s claiming that be eggs equals zero. So let&#x27;s see what would happen if we substituted these values into our quadratic formula. Well, we would have XT equals negative B plus or minus the square. Root off, I forgot you&#x27;re substituting zero and for B So we have negative zero plus or minus. The square root of zero squared minus four times in this case is too. And see a seven and it&#x27;s all getting divided by two times A. Which is to in this case, well, let&#x27;s see what happens will be simplified us well, having zero in front of our post minus sign adding or subtracting zero doesn&#x27;t change anything, so this doesn&#x27;t actually have to be here now. Inside our radical, we would have zero squared, which is zero. So we have plus or minus the square root of zero. And then when we multiply negative four times two times seven, we get negative 56 and it&#x27;s all getting divided by well, two times two is four. Well, zero minus six is negative 56. So that X equals plus or minus the square with the negative 56 all divided by four. And if we were the simplify this radical because its a negative, we would take out an eye. So indeed this number. So we have plus or minus 56 all over four. So even when we simplify this, we&#x27;re still going to get an imaginary number. So it&#x27;s true when both and you&#x27;re positive? Well, even if I NC were both negative, let&#x27;s pretend it was negative to negative seven. If I had substituted negative values in here a negative four times a negative two times a negative seven would still be negative. 56. Therefore, we would get the same solutions. So I do agree with Emily that the two answers will be imaginary answers and our justification. Like we said, if we substitute two and seven in place of A and C or negative to a negative seven in place to see, we would have gotten imaginary answers.

Jeyasree R T · Answer

Yes, it is possible toe add a serial number on an imaginary number. For example, Considered a real number G on an imaginary number. I be, but this I is the imaginary bumped off it now, adding, these tuna boats will get a blessed by me. And this is the standard form off complex number systems. So I didn&#x27;t really number at an imaginary number. Well, you could result in the complex number.

Problem

In $3-18,$ write each number in terms of $i$ $$ …

Problem 2 Easy Difficulty

Ethan said that the square of any pure imaginary number is a negative real number. Do you agree with Ethan? Justify your answer.

Answer

I agree with Ethan

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Absolute Value - Example 1

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I agree with Ethan

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Ann Xavier GantertAlgebra 2 and Trigonometry

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Ann Xavier Gantert

Algebra 2 and Trigonometry