Multiply $(9-4)(2+5 i)$

The result of multiplying ( 9 − 4 ) ( 2 + 5 i ) is 10 + 25 i .
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Answered by Anonymous | 2025-07-04

Simplify the first term: 9 − 4 = 5 .
Multiply the result by the second term: 5 ( 2 + 5 i ) = 10 + 25 i .
Compare the result with the given options. If the question was ( 9 − 4 i ) ( 2 + 5 i ) , the answer would be 38 + 37 i .
Assuming a typo in the original question, the closest answer is 38 + 37 i ​ .

Explanation

Simplify the expression First, we need to simplify the expression ( 9 − 4 ) ( 2 + 5 i ) .

Simplify the first term We start by simplifying the first term: 9 − 4 = 5 .

Multiply the terms Now we multiply the result by the second term: 5 ( 2 + 5 i ) .

Distribute Distribute the 5: 5 × 2 + 5 × 5 i = 10 + 25 i .

Compare with options Now we compare our result 10 + 25 i with the given options:



− 2 + 37 i
18 − 20 r 2
38 + 37 i
18 + 37 i − 20 i 2 None of the options match our result exactly. However, if we consider that the question might have a typo in the options, we can try to manipulate our result to see if it matches any of them after simplification. The closest option seems to be 18 + 37 i − 20 i 2 . Let's simplify this option, remembering that i 2 = − 1 .
18 + 37 i − 20 i 2 = 18 + 37 i − 20 ( − 1 ) = 18 + 37 i + 20 = 38 + 37 i . This does not match our result.


Re-examine the calculations Let's re-examine our calculations. We have ( 9 − 4 ) ( 2 + 5 i ) = 5 ( 2 + 5 i ) = 10 + 25 i . It seems there was no mistake in our calculation. However, it is possible that the question has an error. If the question was ( 9 − 4 i ) ( 2 + 5 i ) then we would have: ( 9 − 4 i ) ( 2 + 5 i ) = 9 ( 2 ) + 9 ( 5 i ) − 4 i ( 2 ) − 4 i ( 5 i ) = 18 + 45 i − 8 i − 20 i 2 = 18 + 37 i − 20 ( − 1 ) = 18 + 37 i + 20 = 38 + 37 i . In this case, the third option would be correct.

Final Answer Assuming the question was intended to be ( 9 − 4 i ) ( 2 + 5 i ) , the correct answer would be 38 + 37 i . However, based on the original question ( 9 − 4 ) ( 2 + 5 i ) , the correct answer is 10 + 25 i , which is not among the given choices. Since we must choose from the given options, and if we assume there was a typo in the original question, we choose the closest answer, which is 38 + 37 i .


Examples
Complex numbers are used in electrical engineering to represent alternating currents. The multiplication of complex numbers helps in analyzing circuits and understanding the relationships between voltage and current.

Answered by GinnyAnswer | 2025-07-04