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3 votes
Which pair of complex factors results in a real-number product? 15(–15i) 3i(1-3i) (8 + 20i)(–8 – 20i) (4+7i)(4-7i)

2 Answers

0 votes

Answer:

the correct answer is the last one, (4+7i)(4-7i)

Explanation:

User Smaug
by
5.8k points
3 votes

Answer:

(4 + 7i)(4 - 7i)

Explanation:

Factors of the form of a conjugate pair always produce a real number

(a + bi)(a - bi) ← produce a real number product ( a and b are real ), that is

(a + bi)(a - bi) ← expand using FOIL

= a² - bi² ( i² = - 1)

= a² + b² ← a real number

Thus

(4 + 7i)(4 - 7i)

= 16 - 49i²

= 16 + 49 = 65

User Natural
by
5.5k points
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