Question

perform the operation(s) and write the result in standard form. (simplify your (√11 + √12i)(√11 - √12i)

Explanation:

Step1: Recognize the difference of squares formula

The expression \((a + b)(a - b)\) can be simplified using the difference of squares formula \(a^2 - b^2\). Here, let \(a=\sqrt{11}\) and \(b = \sqrt{12}i\).

Step2: Apply the formula

Substitute \(a\) and \(b\) into the formula: \((\sqrt{11})^2-(\sqrt{12}i)^2\).

Step3: Simplify each term

Calculate \((\sqrt{11})^2 = 11\) and \((\sqrt{12}i)^2=(\sqrt{12})^2\times i^2 = 12\times(- 1)=- 12\) (since \(i^2=-1\)).

Step4: Combine the terms

Now, substitute these values back: \(11-(-12)=11 + 12=23\).

Answer:

\(23\)