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
ReIm11−1−122−2−233−3−344−4−455−5−566−6−6z₁ABCD

The Argand diagram shows z₁ = −5 + j2. Click the point that represents z̄₁.

z₁ = −5 + j2
  1. 1A (2 − j5)
  2. 2B (−2 + j5)
  3. 3C (5 − j2)
  4. 4D (−5 − j2)
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 8 − j and z₂ = 2 + j3, find the imaginary part of the product z₁·z₂.

z₁ = 8 − jz₂ = 2 + j3
Im(z₁z₂) =
3.Medium
ReIm22−2−244−4−4z₁z₂w

Given z₁ = 1.5∠150° and z₂ = 4∠110°, find the argument θ of w = z₁/z₂ in degrees, between −180° and 180°.

z₁ = 1.5∠150°z₂ = 4∠110°
θ = °
4.Medium
ReIm11−1−122−2−2θz

Find the argument θ of z = −2 − j in degrees, as the principal value between −180° and 180°.

z = −2 − j
θ = °
5.Hard
ReIm11−1−122−2−2z₁z₂

Solve z² − 5z + 12.5 = 0. The roots are a ± jb; find the real part a.

p = −5q = 12.5
a =
6.Hard
ReIm11−1−122−2−2θz

Find the real part of (−2 + j2)⁴.

z = −2 + j2n = 4
Re(z⁴) =

Answer key

  1. 1. D (−5 − j2)
  2. 2. Im(z₁z₂) = 22
  3. 3. θ = 40 °
  4. 4. θ = −153.4 °
  5. 5. a = 2.5
  6. 6. Re(z⁴) = −64

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