Question
Which of the following shows an expression equivalent to the product of two complex numbers, 5i⋅4i ? (1 point)
Responses
9i
9 i
20
20
4i⋅5i
4 i times 5 i
20i
Responses
9i
9 i
20
20
4i⋅5i
4 i times 5 i
20i
Answers
GPT-4o mini
To find an expression equivalent to the product of the complex numbers \(5i\) and \(4i\), we can calculate the product:
\[
5i \cdot 4i = (5 \cdot 4)(i \cdot i) = 20i^2
\]
Since \(i^2 = -1\), we can substitute that into the expression:
\[
20i^2 = 20(-1) = -20
\]
Now let's evaluate the options provided:
1. **9i** - This does not match our result.
2. **20** - This does not match our result, we found \(-20\).
3. **4i⋅5i** - This is just a different order of multiplication and is equal to \(5i \cdot 4i\), so it represents the original product but does not have a simplified form.
4. **20i** - This does not match our result.
None of the provided options are equivalent to \(-20\), which is the final outcome. However, if we consider the form of the expression before substituting \(i^2\), the option **4i⋅5i** most closely matches the expression derived (as it denotes the same product).
Thus the answer we can select is:
**4i⋅5i**
\[
5i \cdot 4i = (5 \cdot 4)(i \cdot i) = 20i^2
\]
Since \(i^2 = -1\), we can substitute that into the expression:
\[
20i^2 = 20(-1) = -20
\]
Now let's evaluate the options provided:
1. **9i** - This does not match our result.
2. **20** - This does not match our result, we found \(-20\).
3. **4i⋅5i** - This is just a different order of multiplication and is equal to \(5i \cdot 4i\), so it represents the original product but does not have a simplified form.
4. **20i** - This does not match our result.
None of the provided options are equivalent to \(-20\), which is the final outcome. However, if we consider the form of the expression before substituting \(i^2\), the option **4i⋅5i** most closely matches the expression derived (as it denotes the same product).
Thus the answer we can select is:
**4i⋅5i**