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
ReIm55−5−5z₁z₂

For z₁ = 7 − j8 and z₂ = 3 + j4, find the imaginary part of the product z₁·z₂.

z₁ = 7 − j8z₂ = 3 + j4
Im(z₁z₂) =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −3 + j6 and z₂ = 6 − j4, find the modulus of the product, |z₁z₂|.

z₁ = −3 + j6z₂ = 6 − j4
|z₁z₂| =
3.Medium
ReIm55−5−5θz

Find the argument θ of z = −3 − j8 in degrees, as the principal value between −180° and 180°.

z = −3 − j8
θ = °
4.Medium
ReIm22−2−244−4−466−6−6θz

Find the argument θ of z = 3 + j6 in degrees, as the principal value between −180° and 180°.

z = 3 + j6
θ = °
5.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ + 3z² + 7z + 85 = 0 is z₁ = 1 + j4. The coefficients are real. Find the real root r.

z₁ = 1 + j4
r =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ + 3z² − 8z − 30 = 0 is z₁ = −3 + j. The coefficients are real. Find the real root r.

z₁ = −3 + j
r =

Answer key

  1. 1. Im(z₁z₂) = 4
  2. 2. |z₁z₂| = 48.37
  3. 3. θ = −110.6 °
  4. 4. θ = 63.43 °
  5. 5. r = −5
  6. 6. r = 3

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