Question

complex numbers online practice
complete this assessment to review what you’ve learned.
simplify \\((6 - 2i)(6 + 2i)\\). (1 point)
\\(\circ\\) 40
\\(\circ\\) \\(36 - 4i^2\\)
\\(\circ\\) \\(40 + 36i\\)
\\(\circ\\) 32

Explanation:

Step1: Apply difference of squares formula

The expression \((a - b)(a + b)\) can be simplified using the difference of squares formula \(a^2 - b^2\). Here, \(a = 6\) and \(b = 2i\). So, \((6 - 2i)(6 + 2i)=6^2-(2i)^2\).

Step2: Calculate each term

First, calculate \(6^2 = 36\). Then, calculate \((2i)^2 = 2^2\times i^2 = 4\times(- 1)=-4\) (since \(i^2=-1\)).

Step3: Substitute and simplify

Substitute these values back into the formula: \(36-(-4)=36 + 4 = 40\).

Answer:

40