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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.
We need to verify if the product of (2+5i) and (4i-3) is a real number.
Multiply the two terms.
(2 + 5i)(4i - 3)
=> 2*4i + 20*i^2 - 6 - 15i
we know i^2 = -1
=> 8i - 20 - 6 - 15i
=> -7i - 26
This has an imaginary component. The product -7i - 26 of the two complex numbers given is not real.
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