Of course! Let's expand the expression [tex]\((5 - 2i)(5 + 2i)\)[/tex]. This expression is in the form of [tex]\((a - bi)(a + bi)\)[/tex], which is a difference of squares.
Given expression: [tex]\((5 - 2i)(5 + 2i)\)[/tex]
This can be expanded using the formula [tex]\((a - bi)(a + bi) = a^2 - (bi)^2\)[/tex].
1. Identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
- [tex]\(a = 5\)[/tex]
- [tex]\(b = 2\)[/tex]
2. Calculate [tex]\(a^2\)[/tex]:
[tex]\[
a^2 = 5^2 = 25
\][/tex]
3. Calculate [tex]\((bi)^2\)[/tex]:
[tex]\[
(2i)^2 = 4i^2 = 4 \cdot (-1) = -4
\][/tex]
(Remember, [tex]\(i^2 = -1\)[/tex])
4. Substitute these values back into the formula:
[tex]\[
a^2 - (bi)^2 = 25 - (-4)
\][/tex]
5. Simplify the expression:
[tex]\[
25 - (-4) = 25 + 4 = 29
\][/tex]
So, the expanded expression [tex]\((5 - 2i)(5 + 2i)\)[/tex] results in 29.
