Simplify (6−2i)(6+2i)

.(1 point)
Responses

32
32

36−4i2
36 minus 4 i squared

40
40

40+36i

1 answer

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:

\[ \boxed{40} \]