Multiply and simplify the product. (3-5i)(-2+4i) Select the product. 14+2i 14+22i 15+22i 26+2j DOUE

To multiply and simplify the product of \((3-5i)(-2+4i)\), we use the distributive property (also known as the FOIL method for binomials):<br /><br />\[<br />(3-5i)(-2+4i) = 3 \cdot (-2) + 3 \cdot 4i + (-5i) \cdot (-2) + (-5i) \cdot 4i<br />\]<br /><br />Now, calculate each term:<br /><br />1. \(3 \cdot (-2) = -6\)<br />2. \(3 \cdot 4i = 12i\)<br />3. \((-5i) \cdot (-2) = 10i\)<br />4. \((-5i) \cdot 4i = -20i^2\)<br /><br />Since \(i^2 = -1\), we have:<br /><br />\[<br />-20i^2 = -20(-1) = 20<br />\]<br /><br />Now, combine all the terms:<br /><br />\[<br />-6 + 12i + 10i + 20 = 14 + 22i<br />\]<br /><br />So, the simplified product is:<br /><br />\[<br />14 + 22i<br />\]<br /><br />Therefore, the correct answer is:<br /><br />\[<br />14 + 22i<br />\]