Answer:
(1+2i)(1-2i)
Step-by-step 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. [tex](1+2i)(8i)= 8i+16i^{2}[/tex]
=[tex]8i-16[/tex]
B. [tex](1+2i)(2-5i)=2-i-10i^{2}[/tex]
=[tex]12-i[/tex]
C. [tex](1+2i)(1-2i)=1^{2}-4i^{2}[/tex]
=[tex]5[/tex]
D. [tex](1+2i)(4i)=4i+8i^{2}[/tex]
=[tex]4i-8[/tex]
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.
