Answer: The correct option is
(d) \(-24-57i.\)
Step-by-step explanation: We are given to multiply the following two complex numbers :
\((6-7i)(3-6i).\)
To multiply the given complex numbers, we need to multiply the real and imaginary parts of one complex number number with the real and imaginary parts of the other.
The multiplication is as follows :
\((6-7i)(3-6i)\\\\=6(3-6i)-7i(3-6i)\\\\=18-36i-21i+42i^2\\\\=18-57i+42\times(-1)~~~~~~~~~~~~~~~~~~~~~~[\textup{since }i^2=-1]\\\\=18-57i-42\\\\=-24-57i.\)
Thus, the required multiplied form is \(-24-57i.\)
Option (d) is CORRECT.
