Answer :
To find the expression or value equivalent to [tex]\((8 + 2i)(8 - 2i)\)[/tex], we need to expand and simplify this complex number multiplication step-by-step.
Given:
[tex]\((8 + 2i)(8 - 2i)\)[/tex]
We can use the difference of squares formula [tex]\( (a + b)(a - b) = a^2 - b^2 \)[/tex]:
1. Here, [tex]\(a = 8\)[/tex] and [tex]\(b = 2i\)[/tex].
2. Substitute these values into the formula:
[tex]\[
(8 + 2i)(8 - 2i) = 8^2 - (2i)^2
\][/tex]
3. Calculate [tex]\(8^2\)[/tex]:
[tex]\[
8^2 = 64
\][/tex]
4. Calculate [tex]\((2i)^2\)[/tex]:
[tex]\[
(2i)^2 = 4i^2
\][/tex]
5. Remember that [tex]\(i^2 = -1\)[/tex]:
[tex]\[
4i^2 = 4(-1) = -4
\][/tex]
6. Substitute these results back into the expression:
[tex]\[
(8 + 2i)(8 - 2i) = 64 - (-4)
\][/tex]
7. Simplify the expression:
[tex]\[
64 - (-4) = 64 + 4 = 68
\][/tex]
Therefore, the expression or value equivalent to [tex]\((8 + 2i)(8 - 2i)\)[/tex] is [tex]\(68\)[/tex].
Given:
[tex]\((8 + 2i)(8 - 2i)\)[/tex]
We can use the difference of squares formula [tex]\( (a + b)(a - b) = a^2 - b^2 \)[/tex]:
1. Here, [tex]\(a = 8\)[/tex] and [tex]\(b = 2i\)[/tex].
2. Substitute these values into the formula:
[tex]\[
(8 + 2i)(8 - 2i) = 8^2 - (2i)^2
\][/tex]
3. Calculate [tex]\(8^2\)[/tex]:
[tex]\[
8^2 = 64
\][/tex]
4. Calculate [tex]\((2i)^2\)[/tex]:
[tex]\[
(2i)^2 = 4i^2
\][/tex]
5. Remember that [tex]\(i^2 = -1\)[/tex]:
[tex]\[
4i^2 = 4(-1) = -4
\][/tex]
6. Substitute these results back into the expression:
[tex]\[
(8 + 2i)(8 - 2i) = 64 - (-4)
\][/tex]
7. Simplify the expression:
[tex]\[
64 - (-4) = 64 + 4 = 68
\][/tex]
Therefore, the expression or value equivalent to [tex]\((8 + 2i)(8 - 2i)\)[/tex] is [tex]\(68\)[/tex].
