Option A: -24 is the coefficient of i
Explanation:
The expression is ![(6-2 i)^{2}](https://tex.z-dn.net/?f=%286-2%20i%29%5E%7B2%7D)
To determine the coefficient of i, first we shall find the square of the binomial for the expression ![(6-2 i)^{2}](https://tex.z-dn.net/?f=%286-2%20i%29%5E%7B2%7D)
The formula to find the square of the binomial for this expression is given by
![(a-b)^{2}=a^{2}-2 a b+b^{2}](https://tex.z-dn.net/?f=%28a-b%29%5E%7B2%7D%3Da%5E%7B2%7D-2%20a%20b%2Bb%5E%7B2%7D)
where
and ![b=2i](https://tex.z-dn.net/?f=b%3D2i)
Substituting this value and expanding, we get,
![(6-2 i)^{2}=6^{2} -2(6)(2i)+(2i)^{2}](https://tex.z-dn.net/?f=%286-2%20i%29%5E%7B2%7D%3D6%5E%7B2%7D%20-2%286%29%282i%29%2B%282i%29%5E%7B2%7D)
Simplifying the terms, we have,
![(6-2 i)^{2}=36-24i-4](https://tex.z-dn.net/?f=%286-2%20i%29%5E%7B2%7D%3D36-24i-4)
Thus, from the above expression the coefficient of i is determined as -24.
Hence, Option A is the correct answer.