What is the value of the product 3 2i multiplied by 3 2i?

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To find the value of the product of the complex numbers 3 + 2i and 3 + 2i, we will use the distributive property (also known as the FOIL method when dealing with binomials).

First, we rewrite the expression:

(3 + 2i) × (3 + 2i)

Now, we apply the distributive property:

  • First terms: 3 × 3 = 9
  • Outer terms: 3 × 2i = 6i
  • Inner terms: 2i × 3 = 6i
  • Last terms: 2i × 2i = 4i²

Now we combine the results:

9 + 6i + 6i + 4i²

Since i² = -1, we can substitute this into our equation:

4i² = 4(-1) = -4

thus:

9 + 6i + 6i – 4

Combining like terms:

(9 – 4) + (6i + 6i) = 5 + 12i

Therefore, the value of the product (3 + 2i) × (3 + 2i) is 5 + 12i.

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