Match the complex expressions on the left with the correct simplified value on the right. (8+2i)-(8+i) (2+5i)(1+4i) (8+2i)+(3-4i) (2-2i)(6-3i) i -18+13i 6-18i 11-2i

Let's match each complex expression with its simplified value step by step.<br /><br />1. \((8+2i)-(8+i)\)<br /> \[<br /> = 8 + 2i - 8 - i<br /> = 0 + i<br /> = i<br /> \]<br /> So, \((8+2i)-(8+i)\) matches with \(i\).<br /><br />2. \((2+5i)(1+4i)\)<br /> \[<br /> = 2 \cdot 1 + 2 \cdot 4i + 5i \cdot 1 + 5i \cdot 4i<br /> = 2 + 8i + 5i + 20i^2<br /> = 2 + 13i + 20(-1)<br /> = 2 + 13i - 20<br /> = -18 + 13i<br /> \]<br /> So, \((2+5i)(1+4i)\) matches with \(-18+13i\).<br /><br />3. \((8+2i)+(3-4i)\)<br /> \[<br /> = 8 + 2i + 3 - 4i<br /> = 11 - 2i<br /> \]<br /> So, \((8+2i)+(3-4i)\) matches with \(11-2i\).<br /><br />4. \((2-2i)(6-3i)\)<br /> \[<br /> = 2 \cdot 6 + 2 \cdot (-3i) - 2i \cdot 6 - 2i \cdot (-3i)<br /> = 12 - 6i - 12i + 6i^2<br /> = 12 - 18i + 6(-1)<br /> = 12 - 18i - 6<br /> = 6 - 18i<br /> \]<br /> So, \((2-2i)(6-3i)\) matches with \(6-18i\).<br /><br />Now, let's match the simplified values with the expressions:<br /><br />- \(i\) matches with \((8+2i)-(8+i)\)<br />- \(-18+13i\) matches with \((2+5i)(1+4i)\)<br />- \(6-18i\) matches with \((2-2i)(6-3i)\)<br />- \(11-2i\) matches with \((8+2i)+(3-4i)\)<br /><br />So the final matches are:<br /><br />1. \((8+2i)-(8+i)\) matches with \(i\)<br />2. \((2+5i)(1+4i)\) matches with \(-18+13i\)<br />3. \((8+2i)+(3-4i)\) matches with \(11-2i\)<br />4. \((2-2i)(6-3i)\) matches with \(6-18i\)