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 = 8 + j and z₂ = 3 + j2, find the real part of the quotient z₁/z₂.

z₁ = 8 + jz₂ = 3 + j2
Re(z₁/z₂) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −5 − j and z₂ = −5 − j4, find the modulus of the quotient, |z₁/z₂|.

z₁ = −5 − jz₂ = −5 − j4
|z₁/z₂| =
3.Medium
ReIm11−1−122−2−2z₁z₂w

Given z₁ = 2∠70° and z₂ = 0.5∠−140°, find the real part of w = z₁·z₂.

z₁ = 2∠70°z₂ = 0.5∠−140°
Re(w) =
4.Medium
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−8zABCD

The diagram shows z = −3 − j2. With w = 0.5∠−90°, click the point that represents z/w.

z = −3 − j2w = 0.5∠−90°
  1. 1A (−6 − j4)
  2. 2B (4 − j6)
  3. 3C (−4 + j6)
  4. 4D (2 − j3)
5.Hard
ReIm0.50.5−0.5−0.511−1−1θz

Use De Moivre's theorem to find the imaginary part of z⁹ for z = −1 + j.

z = −1 + jn = 9
Im(z⁹) =
6.Hard
ReIm11−1−122−2−2z₀z₁z₂z₃

The roots of zⁿ = w with n = 4 and w = 16∠−120° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2, 3. Find the imaginary part of z₂.

w = 16∠−120°n = 4k = 2
Im(z₂) =

Answer key

  1. 1. Re(z₁/z₂) = 2
  2. 2. |z₁/z₂| = 0.7963
  3. 3. Re(w) = 0.342
  4. 4. B (4 − j6)
  5. 5. Im(z⁹) = 16
  6. 6. Im(z₂) = 1

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