Question

Simplify (6−2i)(6+2i)
.(1 point)
Responses

32
32

36−4i2
36 minus 4 i squared

40
40

40+36i

Answer 1

To simplify the expression \((6 - 2i)(6 + 2i)\), we can use the fact that it represents a difference of squares:

\[
(a - b)(a + b) = a^2 - b^2
\]

Here, \(a = 6\) and \(b = 2i\). Therefore:

\[
(6 - 2i)(6 + 2i) = 6^2 - (2i)^2
\]

Calculating \(6^2\):

\[
6^2 = 36
\]

Now, calculate \((2i)^2\):

\[
(2i)^2 = 4i^2
\]

Since \(i^2 = -1\), we have:

\[
4i^2 = 4(-1) = -4
\]

Now, substituting back, we get:

\[
36 - (-4) = 36 + 4 = 40
\]

So, the simplified expression is:

\[
\boxed{40}
\]