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Which of the following complex numbers i...

Which of the following complex numbers is equivalent to
`(3-5i)/(8+2i)`? (Note: `i=sqrt(-1)`)

A

`(3)/(8)-(5i)/(2)`

B

`(3)/(8)+(5i)/(2)`

C

`(7)/(34)-(23i)/(34)`

D

`(7)/(34)+(23i)/(34)`

Text Solution

AI Generated Solution

To simplify the complex number \((3-5i)/(8+2i)\), we will follow these steps: ### Step 1: Rationalize the denominator To eliminate the imaginary part in the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is \(8 - 2i\). \[ \frac{3-5i}{8+2i} \cdot \frac{8-2i}{8-2i} \] ...
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