Question

simplify.
(6 + 9i)²
write your answer in the form a + bi.

Explanation:

Step1: Recall the formula for squaring a binomial

The formula \((a + b)^2 = a^2 + 2ab + b^2\). Here, \(a = 6\) and \(b = 9i\).

Step2: Calculate each term

First, calculate \(a^2\): \(6^2 = 36\).
Then, calculate \(2ab\): \(2\times6\times9i = 108i\).
Next, calculate \(b^2\): \((9i)^2 = 81i^2\). Since \(i^2=- 1\), \(81i^2=81\times(-1)=-81\).

Step3: Combine the terms

Now, add the three terms together: \(36 + 108i-81\).
Combine the real parts: \(36-81=-45\).
So the expression becomes \(-45 + 108i\).

Answer:

\(-45 + 108i\)