Question

Which pair of complex numbers has a real-number product? (1 2i)(8i) (1 2i)(2 – 5i) (1 2i)(1 – 2i) (1 2i)(4i)

Answer 1

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 brainly.com/question/10662770

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