Respuesta :
The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.
According to the statement
we have given Following are the pairs of the complex number:
(1+2i)(8i),
(1 + 2i)(2 – 5i)
(1+2i)(1-2i) and (1+2i)(4i)
We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".
So, For this purpose
we have to multiply these pairs with each other.
So,
(1+2i)(8i) = 8i +16(i)^2
And
(1 + 2i)(2 – 5i) = 2 +4i - 5i +10(i)^2
And
(1+2i)(1-2i) = 1 -4(i)^2 -2i +2i = 1+4 = 5
And
(1+2i)(4i) = 4i + 6(i)^2
From these multiplication we found that the third pair have a real number product.
So, The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.
Learn more about Complex Number here https://brainly.com/question/10662770
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