The expression you've written is \((2 + 3i)^2\), where \(i\) represents the imaginary unit, defined by \(i^2 = -1\).

To solve this, let's use the formula for expanding a binomial \((a + b)^2 = a^2 + 2ab + b^2\).

Here, \(a = 2\) and \(b = 3i\):

\[
(2 + 3i)^2 = 2^2 + 2(2)(3i) + (3i)^2
\]

Now, let's simplify each part:

\[
2^2 = 4
\]
\[
2(2)(3i) = 12i
\]
\[
(3i)^2 = 9i^2 = 9(-1) = -9
\]

Now, combine everything:

\[
4 + 12i - 9 = -5 + 12i
\]

So, \((2 + 3i)^2 = -5 + 12i\).

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Do you want more details or have any questions?

Here are some related questions you might find interesting:
1. What is the general form of the square of any complex number \( (a + bi)^2 \)?
2. How can complex numbers be represented on the Argand plane?
3. What is the geometric meaning of squaring a complex number?
4. How do you multiply two complex numbers?
5. What is the modulus of \( 2 + 3i \)?

**Tip:** When squaring complex numbers, always remember that \(i^2 = -1\) to handle the imaginary unit correctly.

Learn how to square the complex number (2 + 3i) using binomial expansion and key properties of imaginary numbers, including the fact that i^2 = -1. This problem covers concepts like complex number multiplication and is suitable for students in Grades 10-12.

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