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NY Regents Algebra II Complex Numbers — practice questions

Explore 6 free Complex Numbers questions in NY Regents Algebra II Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Complex Numbers questions and exercises with answers

Showing questions 1–6 of 6.

The imaginary unit i is defined as the square root of which number?Read the answer and worked solution →In the complex number 7 + 4i, which part is the real part?Read the answer and worked solution →Add the complex numbers 5 - 2i and 3 + 7i. What is the sum?Read the answer and worked solution →How is the complex conjugate of a complex number obtained?Read the answer and worked solution →Multiply (2 + 3i) by (4 - i). What is the product in standard form?Read the answer and worked solution →Simplify i raised to the power 27. What is the result?Read the answer and worked solution →

Worked practice questions

The imaginary unit i is defined as the square root of which number?

  1. Negative one
  2. Positive one
  3. Negative four
  4. Positive four
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Correct answer: A. Negative one

1. Square roots of negative numbers are not real numbers. 2. To handle them, one new number is defined as the square root of negative 1, and it is named i. 3. Squaring that definition gives i squared equal to negative 1, which is what makes the system work. _Source: OpenStax Precalculus (CC BY 4.0), section 3.1 Complex Numbers_

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In the complex number 7 + 4i, which part is the real part?

  1. The number 4i
  2. The number 7
  3. The number 4
  4. The number 11
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Correct answer: B. The number 7

1. Standard form for a complex number is a + bi. 2. In that form a is the real part and bi is the imaginary part. 3. Matching 7 + 4i against a + bi gives a equal to 7, so the real part is 7. _Source: OpenStax Precalculus (CC BY 4.0), section 3.1 Complex Numbers_

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Add the complex numbers 5 - 2i and 3 + 7i. What is the sum?

  1. 8 - 5i
  2. 2 + 5i
  3. 8 + 5i
  4. 15 - 14i
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Correct answer: C. 8 + 5i

1. Adding complex numbers combines the real parts and combines the imaginary parts separately. 2. The real parts give 5 plus 3, which is 8. 3. The imaginary parts give negative 2 plus 7, which is 5. 4. So the sum is 8 + 5i, and subtracting instead would have given 2 - 9i. _Source: OpenStax Precalculus (CC BY 4.0), section 3.1 Complex Numbers_

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More Mathematics topics

Exponential and Logarithmic ModelsGraphs of Polynomial FunctionsPower and Polynomial FunctionsRational FunctionsZeros of Polynomial FunctionsProperties of LogarithmsQuadratic FunctionsDividing Polynomials