Which pair of complex numbers has a real number product

Posted By Admin @ September 03, 2022



Which pair of complex numbers has a real-number product?
(1 + 3i)(6i)
(1 + 3i)(2 – 3i)
(1 + 3i)(1 – 3i)
(1 + 3i)(3i)


we will proceed to verify each case to determine the solution

remember that

i^{2} =-1

case A) (1 + 3i)(6i)

applying distributive property

(1 + 3i)(6i)=1*6i+3i*6i \\=6i+18i^{2}\\=6i+18*(-1)\\=6i-18

-18+6i ------> is not a real number


the case A) is not a real number product

case B) (1 + 3i)(2-3i)

applying distributive property

(1 + 3i)(2-3i)=1*2+1*(-3i)+3i*(2)+3i*(-3i)\\=2-3i+6i-9i^{2}\\=2+3i-9*(-1) \\=11+3i

11+3i ------> is not a real number


the case B) is not a real number product  

case C) (1 + 3i)(1-3i)

applying difference of square

(1 + 3i)(1-3i)=(1)^{2}-(3i)^{2}\\=1-9i^{2}\\=1-9*(-1) \\=10

10 ------> is a real number


the case C) is  a real number product  

case D) (1 + 3i)(3i)

applying distributive property

(1 + 3i)(3i)=1*3i+3i*3i \\=3i+9i^{2}\\=3i+9*(-1) \\=3i-9

-9+3i ------> is not a real number


the case D) is not a real number product

the answer is

(1 + 3i)(1-3i)


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