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 = −5 − j4 and z₂ = 2 + j, find the modulus of the product, |z₁z₂|.

z₁ = −5 − j4z₂ = 2 + j
|z₁z₂| =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −4 − j2 and z₂ = 1 − j4, find the real part of the product z₁·z₂.

z₁ = −4 − j2z₂ = 1 − j4
Re(z₁z₂) =
3.Medium
ReIm22−2−244−4−4z₁z₂w

Given z₁ = 2∠150° and z₂ = 4∠110°, find the imaginary part of w = z₁/z₂.

z₁ = 2∠150°z₂ = 4∠110°
Im(w) =
4.Medium
ReIm22−2−244−4−4z₁z₂w

Given z₁ = 1.5∠−35° and z₂ = 3∠−50°, find the imaginary part of w = z₁·z₂.

z₁ = 1.5∠−35°z₂ = 3∠−50°
Im(w) =
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 8z + 32 = 0. The roots are a ± jb; find b > 0.

p = 8q = 32
b =
6.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 6z + 25 = 0. The roots are a ± jb; find b > 0.

p = 6q = 25
b =

Answer key

  1. 1. |z₁z₂| = 14.32
  2. 2. Re(z₁z₂) = −12
  3. 3. Im(w) = 0.3214
  4. 4. Im(w) = −4.483
  5. 5. b = 4
  6. 6. b = 4

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