Question

simplify.
(-2 + 9i)(-2 - 9i)
write your answer in the form a + bi.

Explanation:

Step1: Use the difference of squares formula \((a + b)(a - b)=a^2 - b^2\)

Here, \(a=-2\) and \(b = 9i\), so \((-2 + 9i)(-2 - 9i)=(-2)^2-(9i)^2\)

Step2: Calculate each term

First, \((-2)^2 = 4\). Second, \((9i)^2=9^2\times i^2 = 81\times(- 1)=-81\) (since \(i^2=-1\))

Step3: Substitute back and simplify

\(4-(-81)=4 + 81=85\)

Answer:

\(85+0i\)