Question

Which pair of complex numbers has a real-number product?

A) (1 + 21)(81)
B) (1 + 21)(2 - 51)
C) (1 + 21)(1 - 21)
D) (1 + 21)(41)

Answer 1

The pair of complex numbers with a real-number product is (1 + 21)(1 - 21).

Step-by-step explanation:

To determine which pair of complex numbers has a real-number product, we need to multiply each pair of complex numbers.

Let's evaluate each option:

1. (1 + 21)(81) = 0 + 21(81) = 1701 --> not a real number
2. (1 + 21)(2 - 51) = 22 - 51 + 462i - 51i = -29 + 411i --> not a real number
3. (1 + 21)(1 - 21) = 0 + 20(1) - 21(21) = -441 --> real number
4. (1 + 21)(41) = 42 + 462i --> not a real number

So, the pair of complex numbers with a real-number product is (1 + 21)(1 - 21), also known as option C.