Perform the operation and write the result in standard form. (Simplify your answer completely.) (sqrt (3)+4i)(sqrt (3)-4i) square se

To perform the operation \((\sqrt{3} + 4i)(\sqrt{3} - 4i)\), we can use the difference of squares formula, which states that \((a + b)(a - b) = a^2 - b^2\).<br /><br />Here, \(a = \sqrt{3}\) and \(b = 4i\).<br /><br />So, we have:<br />\[<br />(\sqrt{3} + 4i)(\sqrt{3} - 4i) = (\sqrt{3})^2 - (4i)^2<br />\]<br /><br />Now, calculate each term separately:<br />\[<br />(\sqrt{3})^2 = 3<br />\]<br />\[<br />(4i)^2 = 16i^2<br />\]<br /><br />Since \(i^2 = -1\), we have:<br />\[<br />16i^2 = 16(-1) = -16<br />\]<br /><br />Putting it all together:<br />\[<br />3 - (-16) = 3 + 16 = 19<br />\]<br /><br />Therefore, the result in standard form is:<br />\[<br />\boxed{19}<br />\]