Algebra 2 Complex Conjugates and Complex Solutions Test with Point Values (PDF)

Algebra 2 math test: Complex Conjugates and Complex Solutions – Maths PDF

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This complex conjugates test for Algebra 2 covers complex conjugates and complex solutions (Common Core N-CN.A.3, N-CN.C.7), with a free PDF to print.

This 45-minute test on complex conjugates, division and complex solutions 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 Conjugates and Complex Solutions
Standards: N-CN.A.3, N-CN.C.7
Time: 45 minutes
Total: 20 points

Complex conjugates test: questions

Question 1 – Conjugate and modulus [2 pts]

The point z.

The point \(z\) is shown. Write \(z\), its conjugate, and \(|z|\).

Question 2 – Divide [3 pts]

Divide and write each result in \(a + bi\) form.

\(\frac{7 + i}{1 – i}\) (2 points)
\(\frac{2 – 3i}{i}\) (1 point)

Question 3 – Quadratic formula [3 pts]

Solve \(x^{2} – 2x + 5 = 0\) and \(x^{2} + 16 = 0\). (2 points) and (1 point)

Question 4 – Count real solutions [2 pts]

y = x² + 6x + 11

The graph of \(y = x^{2} + 6x + 11\) is shown. State how many real solutions \(x^{2} + 6x + 11 = 0\) has, then confirm with the discriminant.

Question 5 – Write the equation [2 pts]

Write a quadratic equation with real coefficients and solutions \(1 + 4i\) and \(1 – 4i\).

Question 6 – Impedance [2 pts]

Z = V ÷ I

Voltage is \(12 + 16i\) volts and current is \(2 + i\) amps. Find the impedance \(Z = V \div I\).

Question 7 – Modulus of a product [2 pts]

Let \(z = 1 + 2i\). Find \(z \cdot \overline{z}\) and compare it with \(|z|^{2}\).

Question 8 – Projectile [2 pts]

The height of a ball is \(h = -16t^{2} + 48t\) feet. Can it reach 40 feet? Set \(h = 40\) and use the discriminant.

Question 9 – Solve with a leading coefficient [2 pts]

Solve \(3x^{2} – 6x + 7 = 0\).

Key facts behind this complex conjugates test

Key facts

The conjugate of a + bi is a – bi.
z times its conjugate = a² + b², a real number.
The modulus |a + bi| = √(a² + b²).
Divide by multiplying top and bottom by the conjugate of the denominator.
A negative discriminant gives a pair of complex conjugate solutions.

How to use this complex conjugates 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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