Question
Which of the following shows an expression equivalent to the product of two complex numbers, 5iā
4i ? (1 point) Responses 20i 20 i 4iā
5i 4 i times 5 i 20 20 9i
Answers
Answered by
oobleck
since 20 was included twice in the options, I'd say there was a typo, and the correct choice of -20 was just mistyped.
Answered by
GPT-4o mini
To find an expression equivalent to the product of \(5i\) and \(4i\), we can first multiply these complex numbers together.
\[
5i \cdot 4i = (5 \cdot 4)(i \cdot i) = 20i^2
\]
Since \(i^2 = -1\), we can substitute that in:
\[
20i^2 = 20 \cdot (-1) = -20
\]
Thus, the product \(5i \cdot 4i\) simplifies to \(-20\).
Now, from the options provided, we need to check which corresponds to this result. The only expression that would reasonably relate to this calculation is:
- \(20i\) does not equal \(-20\).
- \(20\) does not equal \(-20\).
- \(9i\) does not equal \(-20\).
- \(4i \cdot 5i\) simply rearranges the multiplication but does not equal \(-20\) as an expression itself.
Therefore, there seems to be no direct option that indicates the result is \(-20\).
If you require a choice from the given responses strictly for the multiplication process, \(4i \cdot 5i\) is equivalent to \(5i \cdot 4i\), though neither reflects the result of the multiplication accurately as \(-20\).
So the answer, based on the multiplication expression, is:
**4i ā 5i (which simply shows the rearrangement of the multiplication and does not provide the numerical result of -20)**.
\[
5i \cdot 4i = (5 \cdot 4)(i \cdot i) = 20i^2
\]
Since \(i^2 = -1\), we can substitute that in:
\[
20i^2 = 20 \cdot (-1) = -20
\]
Thus, the product \(5i \cdot 4i\) simplifies to \(-20\).
Now, from the options provided, we need to check which corresponds to this result. The only expression that would reasonably relate to this calculation is:
- \(20i\) does not equal \(-20\).
- \(20\) does not equal \(-20\).
- \(9i\) does not equal \(-20\).
- \(4i \cdot 5i\) simply rearranges the multiplication but does not equal \(-20\) as an expression itself.
Therefore, there seems to be no direct option that indicates the result is \(-20\).
If you require a choice from the given responses strictly for the multiplication process, \(4i \cdot 5i\) is equivalent to \(5i \cdot 4i\), though neither reflects the result of the multiplication accurately as \(-20\).
So the answer, based on the multiplication expression, is:
**4i ā 5i (which simply shows the rearrangement of the multiplication and does not provide the numerical result of -20)**.
Answered by
GPT-4o mini
It's quite possible that there was a typo in the options provided. Given the calculations we performed, the product of \(5i\) and \(4i\) is indeed \(-20\), and if that option were available, it would be the correct answer.
If "20" was written twice, and one of those instances was intended to represent \(-20\), then that would rightly suggest that the correct choice should be \(-20\).
So you are correct in interpreting that if the option "-20" exists or was intended, it would be the accurate expression for the product of \(5i\) and \(4i\). If you have further questions or need more clarification, feel free to ask!
If "20" was written twice, and one of those instances was intended to represent \(-20\), then that would rightly suggest that the correct choice should be \(-20\).
So you are correct in interpreting that if the option "-20" exists or was intended, it would be the accurate expression for the product of \(5i\) and \(4i\). If you have further questions or need more clarification, feel free to ask!