Real and Complex Numbers: Algebra 2 Math Test – PDF Download

Question 1: Classify marked numbers (2 points)

Two numbers are marked on the number line.

1. Is each number rational or irrational? (1 point)
2. Name the smallest of these sets that contains each number: natural, integer, rational, irrational. (1 point)

Question 2: Points in the complex plane (2 points)

Write the complex number for each point shown.

1. Point M (1 point)
2. Point N (1 point)

Question 3: Imaginary unit (2 points)

1. Simplify \(\sqrt{-72}\). (1 point)
2. Solve \(3x^{2}+48=0\). (1 point)

Question 4: Add and subtract (2 points)

Write each result in the form \(a+bi\).

1. \((5-3i)+(-8+7i)\) (1 point)
2. \((6+2i)-(9-5i)\) (1 point)

Question 5: Multiply (3 points)

Write each product in the form \(a+bi\).

1. \((4-i)(2+3i)\) (1 point)
2. \((3+5i)^{2}\) (1 point)
3. \((7+2i)(7-2i)\) (1 point)

Question 6: Powers of i (2 points)

Simplify.

1. \(i^{38}\) (1 point)
2. \(i^{83}\) (1 point)

Question 7: Arrows in the plane (3 points)

The arrows show two complex numbers \(z_1\) and \(z_2\).

1. Write \(z_1\) and \(z_2\) in the form \(a+bi\). (1 point)
2. Find \(z_1+z_2\). (1 point)
3. Find \(z_1-z_2\). (1 point)

Question 8: Check a solution (2 points)

Show that \(2+i\) is a solution of \(x^{2}-4x+5=0\).

Question 9: Find the error (2 points)

Liam writes \((2+3i)(2-3i)=4-9i^{2}=4-9=-5\). Find his mistake and give the correct product.

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