Answer: the correct option is (C) \(38+37i.\)
Step-by-step explanation: We are given to multiply the following two complex numbers :
\((9-4i)(2+5i).\)
To multiply the above complex numbers, we need to multiply the real and imaginary parts of first complex number with the real and imaginary parts of the second complex number.
The multiplication is as follows :
\((9-4i)(2+5i)\\\\=9(2+5i)-4i(2+5i)\\\\=18+45i-8i-20i^2\\\\=18+(45-8)i-20\times (-1)~~~~~~~~~~~~~~~~~~~~[\textup{since }i^2=-1]\\\\=18+37i+20\\\\=38+37i.\)
Thus, the required product is \(38+37i.\)
Option (C) is CORRECT.
