Question

multiply $(-10 + 5i)(-10 - 5i)$. (1 point)

Explanation:

Step1: Recognize the formula

This is a product of a sum and a difference, which follows the formula \((a + b)(a - b)=a^2 - b^2\). Here, \(a=- 10\) and \(b = 5i\).

Step2: Apply the formula

First, calculate \(a^{2}\): \((-10)^{2}=100\).
Then, calculate \(b^{2}\): \((5i)^{2}=25i^{2}\). Since \(i^{2}=-1\), then \(25i^{2}=25\times(-1)=- 25\).
Now, substitute into the formula \(a^{2}-b^{2}\): \(100-(-25)=100 + 25\).

Step3: Calculate the result

\(100+25 = 125\).

Answer:

\(125\)