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