Question

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

Explanation:

Step1: Recall the power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((-9i)^2\), we can apply this rule as \((-9)^2\times i^2\).

Step2: Calculate \((-9)^2\) and \(i^2\)

We know that \((-9)^2 = 81\) and by the definition of the imaginary unit \(i\), \(i^2=-1\).

Step3: Multiply the results

Now we multiply these two results: \(81\times(-1)= - 81\). In the form \(a + bi\), this is \(-81+0i\).

Answer:

\(-81 + 0i\)