Answer: The correct option is
(C) 56-5i.
Step-by-step explanation: We are given to simplify the following product of complex numbers :
[tex]P=(10+3i)(5-2i)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To simplify the given product, we must multiply each term of the first factor each term of the second factor and will be using the following vale of i :
[tex]i=\sqrt{-1}~~~~\Rightarrow i^2=-1.[/tex]
From (i), we get
[tex]P\\\\=(10+3i)(5-2i)\\\\=10(5-2i)+3i(5-2i)\\\\=50-20i+15i-6i^2\\\\=50-5i-6(-1)\\\\=50-5i+6\\\\=56-5i.[/tex]
Thus, the required simplified form is 56-5i.
Option (C) is CORRECT.
