Complex numbers worksheet with answers

Free printable Complex numbers worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
ReIm11−1−122−2−233−3−344−4−455−5−566−6−6z₁z₂ABCD

The Argand diagram shows z₁ = −3 + j4 and z₂ = 1 + j. Click the point that represents z₁ − z₂.

z₁ = −3 + j4z₂ = 1 + j
  1. 1A (−2 + j5)
  2. 2B (−4 + j3)
  3. 3C (−4 − j3)
  4. 4D (4 − j3)
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 5 + j6 and z₂ = 5 + j4, find the real part of the product z₁·z₂.

z₁ = 5 + j6z₂ = 5 + j4
Re(z₁z₂) =
3.Medium
ReIm11−1−122−2−2θz

The number z = 2.5·e−j1 has its angle in radians. Find its imaginary part b.

r = 2.5θ = −1 rad
b =
4.Medium
ReIm55−5−5θz

Find the argument θ of z = 7 − j8 in degrees, as the principal value between −180° and 180°.

z = 7 − j8
θ = °
5.Hard
ReIm22−2−244−4−4ABCD

Exactly one of the points A–D is a root of z⁶ = 64∠90°. Click it.

w = 64∠90°n = 6
  1. 1A (2∠105°)
  2. 2B (3.6∠105°)
  3. 3C (2∠−75°)
  4. 4D (2∠75°)
6.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 8z + 18.25 = 0. The roots are a ± jb; find b > 0.

p = 8q = 18.25
b =

Answer key

  1. 1. B (−4 + j3)
  2. 2. Re(z₁z₂) = 1
  3. 3. b = −2.104
  4. 4. θ = −48.81 °
  5. 5. D (2∠75°)
  6. 6. b = 1.5

Full step-by-step solutions: practise this topic on examproblems.com.