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Answer: -3 + 9i
This problem can be written as (1 + 2i)(3+ 3i). Just like with any binomial, you can use FOIL to multiply this out.

F: 1 x 3 = 3
O: 1 x 3i = 3i
I = 2i x 3 = 6i
L = 2i x 3i = 6i^2

When strung together, you get 3 + 3i + 6i + 6i^2, which simplifies to 3 + 9i + 6i^2.  i^2 = -1, since i = √-1. 6 x -1 = -6.

3 + 9i - 6 = -3 + 9i.

The product of r.s is -3+9i.

r = 1+2i ; s = 3+3i
Product of r and s to be determine.

What is complex number?

Any number with representation as a+bi is complex number.

Here,
r.s  = (1+2i)(3+3i)
    = 3+6i+3i+6i²
    = 3+ 9i + 6(-1)   (∵ i²=-1)
    = 3 - 6 +9i
    = -3 + 9i

Thus, the product of r.s is -3+9i.

Learn more about complex number here:
https://brainly.com/question/28007020

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