Question

simplify.
(5 - 2i)(5 + 2i)
? + i

Explanation:

Step1: Use the difference of squares formula

The expression \((a - b)(a + b)=a^2 - b^2\). Here, \(a = 5\) and \(b = 2i\). So we have \((5)^2-(2i)^2\).

Step2: Calculate each term

First, \(5^2 = 25\). Second, \((2i)^2=2^2\times i^2 = 4\times(- 1)=-4\) (since \(i^2=-1\)). Then, \(25-(-4)=25 + 4\).

Step3: Simplify the result

\(25+4 = 29\), and the imaginary part is \(0\) (because there are no terms with \(i\) left). So the expression simplifies to \(29+0i\).

Answer:

\(29 + 0i\)