Final answer:
The square root of 12 is simplified to 2√3, and the square root of -9 is simplified to 3i. Together, they form the complex number 2√3 + 3i. However, if the question is only asking for the imaginary part, the answer would be 3i.
Step-by-step explanation:
To write √12 + √-9 as a complex number, we need to simplify both square roots separately. The square root of 12 can be simplified to 2√3 because 12 is 4 multiplied by 3 and the square root of 4 is 2. However, the square root of a negative number, √-9 in this case, involves the imaginary unit i, since the square root of -1 is defined as i. Therefore, √-9 simplifies to 3i because √9 is 3. Adding these together, 2√3 + 3i, we have a complex number where the real part is 2√3 and the imaginary part is 3i.
In the context of the options provided (a.3i b.2i c.∓3i d.∓2i), it seems there might be an error since none of them correspond to the correct complex number. However, based on the question's phrasing, if we must write only the imaginary part, the correct choice would be a.3i.