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1 vote
What is the standard form of `((2+3i)(4-7i))/((1-i))` ?

A. `-3/13-4/26i`
B. `3/13+4/26i`
C. `31/2+27/2 i`
D. `-31/2-27/2i`

1 Answer

5 votes

Final answer:

The standard form of ((2+3i)(4-7i))/((1-i)) is -7/2+11/2i, which is not one of the provided answer choices.

Step-by-step explanation:

To find the standard form of ((2+3i)(4-7i))/((1-i)), we can start by simplifying the expression in the numerator and denominator. The product of (2+3i) and (4-7i) can be expanded using the FOIL method to obtain 23+2i-21i+12i^2. Simplifying further, we get -9+(-19)i. Dividing this by (1-i) can be done by multiplying the numerator and denominator by the complex conjugate of the denominator, which is (1+i). This gives us (-9+19i)(1+i)/(1-i)(1+i). Expanding this expression and simplifying, we get (-7+11i)/2. Therefore, the standard form of the expression is -7/2+11/2i, which is not one of the provided answer choices.

User Lreeder
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