30 points which pair of complex numbers has a real-number product? (1 + 2i)(8i) (1 + 2i)(2 – 5i) (1 + 2i)(1 – 2i) (1 + 2i)(4i)

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

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

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