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

(1+2i)(1-2i)

Explanation:

Answer 2

(1+2i)(1-2i)

Explanation:

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".

A.
`(1+2i)(8i)= 8i+16i^(2)`

=
`8i-16`

B.
`(1+2i)(2-5i)=2-i-10i^(2)`

=
`12-i`

C.
`(1+2i)(1-2i)=1^(2)-4i^(2)`

=
`5`

D.
`(1+2i)(4i)=4i+8i^(2)`

=
`4i-8`

Since, A,B,D contains the term "i" which means they are not real valued, therefore option C that is (1+2i)(1-2i) has a real number product.