M:N:MC:8

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Additional Topics in Math

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Which of the following is equal to $left parenthesis 14 minus 2 i right parenthesis left parenthesis 7 plus 12 i right parenthesis ?$

(Note: $i equals square root of minus 1 end root$ )

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Correct Answer:

122

Correct Answer:

74 + 154i

Correct Answer:

122 + 154i

Correct Answer:

Yes

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Choice D is correct. Applying the distributive property to multiply the binomials yields the expression $98 plus 168 i minus 14 i minus 24 i squared.$ The note in the stem of the question reminds students that $i equals square root of minus 1 end root comma$ therefore $i squared equals minus 1.$ Substituting this value into the expression gives the student $98 plus 168 i minus 14 i minus left parenthesis minus 24 right parenthesis comma$ and combining like terms results in $122 plus 154 i.$

Choice A is not the correct answer. This answer may result from a combination of errors. The student may not correctly distribute when multiplying the binomials, multiplying only the first terms together and the second terms together. The student may also think that $i squared equals 1.$

Choice B is not the correct answer. This answer may result from a misunderstanding of how to multiply binomials. The distributive property is not applied correctly and the student may only multiply the first two terms together and the last two terms together.

Choice C is not the correct answer. This answer results from misapplying the statement $i equals square root of minus 1 end root.$

Question Difficulty:

medium

Objective:

Students must apply the distributive property on two complex binomials and then simplify the result.

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Question 8 of 18

M:N:MC:8

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