To find the value of the product 3 2i 3 2i, we first need to interpret this expression correctly. It seems to refer to multiplying the complex numbers 3 + 2i and 3 + 2i together.
We can express this mathematically as:
(3 + 2i) * (3 + 2i)
To perform the multiplication, we can use the distributive property (also known as the FOIL method for binomials):
Step 1: Multiply the first terms:
3 * 3 = 9
Step 2: Multiply the outer terms:
3 * 2i = 6i
Step 3: Multiply the inner terms:
2i * 3 = 6i
Step 4: Multiply the last terms:
2i * 2i = 4i²
Since i² is equal to -1, we can rewrite this as:
4i² = 4(-1) = -4
Step 5: Combine all the parts:
9 + 6i + 6i – 4 = 9 – 4 + 12i = 5 + 12i
Therefore, the value of the product 3 + 2i and 3 + 2i is:
5 + 12i