Question

Simplify (10 + 3i)(5 − 2i).

A.) 50 − 5i − 6i2
B.) 44 − 5i
C.) 56 − 5i
D.) 50 − 6i2

Answer 1

The answer I think is D but use the app photo math very useful:)

Answer 2

Answer: The correct option is

(C) 56-5i.

Step-by-step explanation: We are given to simplify the following product of complex numbers :

`P=(10+3i)(5-2i)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

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 :

`i=√(-1)~~~~\Rightarrow i^2=-1.`

From (i), we get

`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.`

Thus, the required simplified form is 56-5i.

Option (C) is CORRECT.