Answer: The final expression in terms of a complex number is -8 + 2i√3. This is the standard form of a complex number, which is expressed as a + bi, where a is the real part and bi is the imaginary part. In this case, a = -8 and b = 2√3.
Explanation:
To write -8 + √-12 as a complex number, we first need to understand that the square root of a negative number can be expressed as a multiple of i, where i is the imaginary unit with the property i^2 = -1.
The square root of -12 is √-12 = √(-1*12) = √-1 * √12 = i√12.
So, -8 + √-12 can be written as -8 + i√12.
However, we can simplify √12 further to 2√3 (since 12 = 4*3 and √4 = 2).
So, the final expression in terms of a complex number is -8 + 2i√3. This is the standard form of a complex number, which is expressed as a + bi, where a is the real part and bi is the imaginary part. In this case, a = -8 and b = 2√3.