Respuesta :

Answer:

(4+7i)(4-7i).

This is because you FOIL it to get:

16 + 28i - 28i -49i^2.

That equals to 16 - 49i^2, which  equals to:

16 + 49

65, which is a real number.

anuksha0456

(4 + 7i)(4 – 7i) is the pair of complex numbers, which on multiplying gives 65, a real number product. Hence, 4th option is the right choice.

What are complex numbers?

Complex numbers are a combination of real numbers and imaginary numbers, which help us to represent the square roots of negative numbers.

It is of the form a + bi, where a and b are real constants, and i = √(-1).

How to solve the question?

In the question, we are asked which pair of given complex numbers will result in a real number product.

To find, we expand each of the given choices as follows:

  • 15(–15i): Multiplying the given numbers, we get -225i, which is a complex number.
  • 3i(1 – 3i): Multiplying the given pairs, we get 3i - 9i² = 3i -9(-1) = 3i + 9 = 3i + 9, which is a complex number. {Using i² = -1}.
  • (8 + 20i)(–8 – 20i): Multiplying the given pairs, we get -(64 + 320i + 400i²) = -(64 + 320i - 400) = 336 - 320i, which is a complex number.
  • (4 + 7i)(4 – 7i): Multiplying the given pairs, we get 16 - 49i² = 16 - 49(-1) = 16 + 49 = 65, which is a real number.

Thus, (4 + 7i)(4 – 7i) is the pair of complex numbers, which on multiplying gives 65, a real number product.

Learn more about complex numbers at

https://brainly.com/question/10662770

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