Question

Multiply (−10+5i)(−10−5i)
(1 point)
Responses

125−100i
125 minus 100 i

125
125

100
100

125+100i

Answer 1

To multiply the complex numbers \((-10 + 5i)(-10 - 5i)\), we can use the formula for the product of two complex numbers:

\[
(a + bi)(c + di) = ac + adi + bci + bdi^2
\]

In this case, \(a = -10\), \(b = 5\), \(c = -10\), and \(d = -5\).

Calculating each term:

1. \(ac = (-10)(-10) = 100\)
2. \(adi = (-10)(-5i) = 50i\)
3. \(bci = (5i)(-10) = -50i\)
4. \(bdi^2 = (5i)(-5i) = -25 \) (since \(i^2 = -1\))

Now, combine the results:

\[
100 + 50i - 50i - 25 = 100 - 25 = 75
\]

Thus, the result of the multiplication is:

\[
75
\]

However, let's also reconsider using the difference of squares, as \( (a + b)(a - b) = a^2 - b^2 \):

Here, \(a = -10\) and \(b = 5i\):

So we calculate:

\[
(-10)^2 - (5i)^2 = 100 - 25(-1) = 100 + 25 = 125
\]

The final answer is \(125\).

Therefore, the correct response is:

**125**