Verify if the result of multiplication (2+5i)(4i-3) is a real number?

To verify the nature of the result, we'll have to remove
the brackets.

For this reason, we'll use the property of
distributivity of multiplication over the
addition.

(2+5i)(4i-3) = 2*(4i-3) +
5i(4i-3)

We'll remove the brackets from the right
side:

(2+5i)(4i-3) = 8i - 6 + 20i^2 -
15i

We'll keep in mind that i^2 = -1 and we'll substitute
in the expression above.

(2+5i)(4i-3) = 8i - 6- 20 -
15i

We'll combine like
terms:

(2+5i)(4i-3) = -26 -
7i

We notice that the result of
multiplication of the given complex numbers is also a complex number: (2+5i)(4i-3) = -26
- 7i.