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
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −5 − j4 and z₂ = 6 + j6, find the real part of the product z₁·z₂.

z₁ = −5 − j4z₂ = 6 + j6
Re(z₁z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −2 − j7 and z₂ = −3 − j3, find the modulus of the product, |z₁z₂|.

z₁ = −2 − j7z₂ = −3 − j3
|z₁z₂| =
3.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = −9 − j5 in degrees, as the principal value between −180° and 180°.

z = −9 − j5
θ = °
4.Medium
ReIm22−2−244−4−4θz

Write z = 5∠160° in rectangular form a + jb and give the imaginary part b.

r = 5θ = 160°
b =
5.Hard
ReIm0.50.5−0.5−0.511−1−1θz

Use De Moivre's theorem to find the real part of z³ for z = −1 + j.

z = −1 + jn = 3
Re(z³) =
6.Hard
ReIm11−1−122−2−2z₀z₁z₂

The roots of zⁿ = w with n = 3 and w = 8∠−90° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2. Find the real part of z₀.

w = 8∠−90°n = 3k = 0
Re(z₀) =

Answer key

  1. 1. Re(z₁z₂) = −6
  2. 2. |z₁z₂| = 30.89
  3. 3. θ = −150.9 °
  4. 4. b = 1.71
  5. 5. Re(z³) = 2
  6. 6. Re(z₀) = 1.732

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