## Expanding (7 + 3i)^2

This article explores the process of expanding the expression **(7 + 3i)^2**, where 'i' represents the imaginary unit (√-1).

### Understanding Complex Numbers

Complex numbers are expressed in the form **a + bi**, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit.

### Expanding the Expression

We can expand (7 + 3i)^2 using the distributive property or by recognizing it as a square of a binomial:

**Method 1: Distributive Property**

(7 + 3i)^2 = (7 + 3i)(7 + 3i)

Expanding using the distributive property:

= 7(7 + 3i) + 3i(7 + 3i) = 49 + 21i + 21i + 9i^2

Since i^2 = -1, we can substitute:

= 49 + 42i - 9
= **40 + 42i**

**Method 2: Square of a Binomial**

(7 + 3i)^2 = (7)^2 + 2(7)(3i) + (3i)^2

Simplifying:

= 49 + 42i + 9i^2
= 49 + 42i - 9
= **40 + 42i**

### Conclusion

Therefore, the expanded form of (7 + 3i)^2 is **40 + 42i**. This process demonstrates how to manipulate complex numbers and simplify expressions involving the imaginary unit.