The expression given can be interpreted as the product of two complex numbers: (3 + 2i)(3 + 2i). To find the value of this product, we can use the formula for the square of a binomial.
Let’s break it down step by step:
- First, recognize that we are multiplying the same complex number by itself: (3 + 2i)(3 + 2i) = (3 + 2i)².
- Using the formula for the square of a binomial, (a + b)² = a² + 2ab + b², where a = 3 and b = 2i, we can substitute:
- Calculate the individual components:
- a² = 3² = 9
- b² = (2i)² = 4i² = 4(-1) = -4
- 2ab = 2 * 3 * 2i = 12i
- Now, combine these results:
- (3 + 2i)² = 9 + 12i – 4
- = 5 + 12i
Thus, the value of the product 3 + 2i and 3 + 2i is: