Chapter 4-6, 4-8 Test, Form A

(4-6) Simplify the following expression.

• 1
• -1
• i
• -i

If r is a positive real number, then

• The above statement is true.
• 
• 

When simplifying the complex expression below...

• A
• B
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• D

What is the complex conjugate of (a - bi)?

• (ai + bi)
• (a - bi)
• (-a + bi)
• (a + bi)

When multiplying complex expressions, what error did the student make in the following:

• There is no error, the student simplified this correctly in standard form.
• The -2i squared should not be negative, but a positive so its 2i squared + 7i + 4 in standard form.
• The -2i squared should not be negative, but a positive so its 2i squared - 7i - 4 in standard form.
• The i squared should be simplified to -1, so it sums with 4 equaling 6, so its standard form is 6 + 7i

Using the Quadratic Formula Above....

• A
• B
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• D

Use the quadratic formula and show your work for the following to get full credit:

• A
• B
• C
• D

What error did the student make in showing their work?

Evaluate responses using AI:

OFF

What error did the student make in showing their work?

• There is no error in calculating with the quadratic formula.
• There was a calculation error, as the square root of 4 should have an I, so its -2i and -4i.
• There is an error in the quadratic formula where it should = positive 2 and 4.
• The error is in the first line. The student needed to subtract 2 from both sides, so standard form reads x squared + 6x + 6 = 0

Choose the best answer for the following question.

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• D