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(1 + 3)(61)

(1 + 3)(2 – 31)

(1 + 31)(1 – 31)

(1 + 31)(3)

we will proceed to verify each case to determine the solution

remember that

case A)

applying distributive property

------> is not a real number

therefore

the case A) is not a real number product

case B)

applying distributive property

------> is not a real number

therefore

the case B) is not a real number product

case C)

applying difference of square

------> is a real number

therefore

the case C) is a real number product

case D)

applying distributive property

------> is not a real number

therefore

the case D) is not a real number product

the answer is

calculating each of the products

noting that i² = (√- 1 )² = - 1

(1 + 2i)(8i) ( distribute by 8i )

= 8i + 16i² = - 16 + 8i ← complex number

(1 + 2i)(2 - 5i) ( expand using FOIL )

= 2 - 5i + 4i - 10i²

= 2 - i + 10 = 12 - i ← complex number

(1 + 2i)(1 - 2i) ( expand using FOIL )

= 1 - 2i + 2i - 4i²

= 1 + 4 = 5 ← real number

(1 + 2i)(4i) ( distribute by 4i )

= 4i +8i² = - 8 + 4i ← complex number

(1 + 2i)(1 - 2i) is the only product which results in a real number

(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.

=

B.

=

C.

=

D.

=

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.

(1 + 3i)(1 – 3i) gives real number product

Step-by-step explanation:

Given the expressions

From analysis one of the following pairs has real-number products

Performing operations on

Performing operations on

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