Algebra 2 Complex Numbers: Adding, Subtracting and Multiplying Test with Point Values (PDF)

Algebra 2 math test: Complex Numbers: Adding, Subtracting and Multiplying – Maths PDF

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This algebra 2 complex numbers test for Algebra 2 covers complex numbers: adding, subtracting and multiplying (Common Core N-CN.A.1, N-CN.A.2), with a free PDF to print.

This 45-minute test on adding, subtracting and multiplying complex numbers has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Complex Numbers: Adding, Subtracting and Multiplying
Standards: N-CN.A.1, N-CN.A.2
Time: 45 minutes
Total: 20 points

Algebra 2 complex numbers test: questions

Question 1 – Imaginary radicals [2 pts]

Simplify \(\sqrt{-64}\). (1 point)
Write \(\sqrt{-75}\) in the form \(bi\) with the radical simplified. (1 point)

Question 2 – Powers of i [2 pts]

Evaluate each power.

\(i^{15}\) (1 point)
\(i^{102}\) (1 point)

Question 3 – Add and subtract [2 pts]

Perform each operation.

\((6 – 3i) + (-2 + 8i)\) (1 point)
\((4 + i) – (9 – 5i)\) (1 point)

Question 4 – Multiply [3 pts]

Multiply and write the answer in \(a + bi\) form.

\((3 + 2i)(1 – 4i)\) (2 points)
\((2 + 7i)(2 – 7i)\) (1 point)

Question 5 – Read the plane [2 pts]

Points A and B.

Write the complex number for each point, then find the sum \(A + B\).

Question 6 – Complex solutions [2 pts]

Solve \(3x^{2} + 48 = 0\) over the complex numbers.

Question 7 – Expression with powers [3 pts]

The number 1 + i.

Simplify \(3i^{2} – 2i^{5} + (1 + i)^{2}\) and write the result in \(a + bi\) form.

Question 8 – Impedance [2 pts]

V = I Z

A circuit has current \(I = 3 – i\) amps and impedance \(Z = 2 + 5i\) ohms. Voltage is \(V = IZ\). Find the voltage in \(a + bi\) form.

Question 9 – Equal complex numbers [2 pts]

Two complex numbers are equal when their real parts are equal and their imaginary parts are equal. Find \(x\) and \(y\) if \((x + 2i) + (3 – yi) = 7 + 5i\).

Key facts behind this algebra 2 complex numbers test

Key facts

The imaginary unit i satisfies i² = -1, so √(-n) = i√n for n > 0.
A complex number a + bi has real part a and imaginary part b.
Add or subtract real parts and imaginary parts separately.
Multiply by distributing, then replace i² with -1.
Powers of i repeat: i, -1, -i, 1.

How to use this algebra 2 complex numbers test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

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