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
ReIm22−2−244−4−4z₁z₂

For z₁ = 3 − j and z₂ = 1 + j5, find the modulus of the product, |z₁z₂|.

z₁ = 3 − jz₂ = 1 + j5
|z₁z₂| =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = 1 − j2 and z₂ = −5 + j3, find the modulus of the product, |z₁z₂|.

z₁ = 1 − j2z₂ = −5 + j3
|z₁z₂| =
3.Medium
ReIm55−5−5z₁z₂w

Given z₁ = 2.5∠55° and z₂ = 3∠110°, find the imaginary part of w = z₁·z₂.

z₁ = 2.5∠55°z₂ = 3∠110°
Im(w) =
4.Medium
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−8zABCD

The diagram shows z = −1 + j3. With w = 2∠−90°, click the point that represents z·w.

z = −1 + j3w = 2∠−90°
  1. 1A (3 + j)
  2. 2B (6 + j2)
  3. 3C (−6 − j2)
  4. 4D (−2 + j6)
5.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z³ = 27∠90°. Click it.

w = 27∠90°n = 3
  1. 1A (1.5∠−90°)
  2. 2B (3∠−30°)
  3. 3C (3∠−60°)
  4. 4D (3∠−90°)
6.Hard
ReIm11−1−122−2−2z₁z₂

One root of z³ + 2z² − 16 = 0 is z₁ = −2 + j2. The coefficients are real. Find the real root r.

z₁ = −2 + j2
r =

Answer key

  1. 1. |z₁z₂| = 16.12
  2. 2. |z₁z₂| = 13.04
  3. 3. Im(w) = 1.941
  4. 4. B (6 + j2)
  5. 5. D (3∠−90°)
  6. 6. r = 2

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