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Which of the following shows an expression equivalent to the product of two complex numbers, 5i⋅4i ? (1 point) Responses 20i 20 i 4i⋅5i 4 i times 5 i 20 20 9i

3 answers

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 ⋅ 5i (which simply shows the rearrangement of the multiplication and does not provide the numerical result of -20).

since 20 was included twice in the options, I'd say there was a typo, and the correct choice of -20 was just mistyped.

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!