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Algebra 2 Imaginary Numbers - Printable Mathematics Worksheets - Wayground

Algebra 2 Imaginary Numbers

10 questions

11th - 11th Grade

Mathematics

Algebra 2 Imaginary Numbers is a Grade 11 mathematics worksheet that helps students simplify square roots of negative numbers and perform operations with imaginary and complex numbers. Across 10 multiple-choice questions, students identify expressions such as √-4, √-23, and √-1 in terms of i, add complex numbers by combining real and imaginary parts, and multiply expressions involving i using accurate distribution and sign rules. This worksheet supports independent practice, guided instruction, or a quick check of students’ fluency with foundational complex-number operations. The multiple-choice format lets teachers identify whether errors come from simplifying negative radicals, handling i, or calculating products such as (4 – 3i)(-7 – 2i). It is a free printable worksheet with a complete answer key for convenient review and grading.

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Worksheets

Algebra 2 Imaginary Numbers

Total questions: 10

Name
Class
Date
1.
Simplify √-4
a)
2i
b)
-2i
c)
2
d)
4i
2.
Simplify √-23
a)
-√23
b)
23i
c)
23
d)
i√23
3.
Simplify √-1
a)
1
b)
-i
c)
-1
d)
i
4.

i6i^6  

a)

1

b)

-1

c)

i

d)

-i

5.

i31i^{31}

a)

1

b)

-1

c)

ii  

d)

−i-i  

6.

i61i^{61}

a)

1

b)

-1

c)

ii  

d)

−i-i  

7.

i89i^{89}

a)

1

b)

-1

c)

ii  

d)

−i-i  

8.
(5-2i) + (-7+8i)
a)
-2+6i
b)
12+6i
c)
-35-16i2
d)
-35 -16i
9.
(3i)(-2+4i)
a)
-6+12i
b)
-12-6i
c)
-2+7i
d)
12+6i
10.
Multiply: 
(4 – 3i)(-7 – 2i)
a)
A.  -23 + 13i
b)
B.  -23 - 29i
c)
C.  -34 + 13i
d)
D.  -34 - 29i
Answer Key

Algebra 2 Imaginary Numbers

Total questions: 10

1.
a) 2i
2.
d) i√23
3.
d) i
4.
b)

-1

5.
d)

−i-i  

6.
c)

ii  

7.
c)

ii  

8.
a) -2+6i
9.
b) -12-6i
10.
c) C.  -34 + 13i

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FAQs

What does the Algebra 2 Imaginary Numbers worksheet cover?

This Grade 11 worksheet uses 10 multiple-choice questions to practise simplifying negative square roots, including √-4, √-23, and √-1, and performing addition and multiplication with imaginary or complex numbers. Students build accuracy with the imaginary unit i, combine real and imaginary terms, and apply distribution when multiplying binomials containing i.

How can I use this worksheet to teach imaginary and complex number operations?

Introduce i by modelling how a negative square root is rewritten, then solve the worksheet’s radical items before moving to addition and multiplication of complex numbers. For the expression-based questions, have students identify the real and imaginary parts first and explain how each answer choice reflects a sign, coefficient, or distribution error. Use the multiple-choice responses as prompts for students to justify why an option is correct rather than relying only on answer selection.

What mistakes should I watch for when students complete this imaginary numbers worksheet?

Students may omit i when simplifying a negative radical, choose the wrong sign for expressions such as √-23, or confuse i with a real number when simplifying √-1. In the addition and multiplication questions, watch for combining unlike real and imaginary terms, distributing incorrectly, and mishandling the negative result produced when i is squared. Reviewing the incorrect choices can help pinpoint whether the error is with radical conversion, signs, or complex-number operations.

How do I assign and grade this imaginary numbers worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can use the 10 multiple-choice items for paper practice or online assessment. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable version also gives schools an option for reducing screen time.

How can I differentiate this complex numbers worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the complex-number expressions and answer choices are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language. These options apply to the worksheet file, including items such as the negative-radical questions and complex-number multiplication problems.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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