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.

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1.Easy
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−8z₁z₂ABCD

The Argand diagram shows z₁ = −1 − j4 and z₂ = −5 + j2. Click the point that represents z₁ + z₂.

z₁ = −1 − j4z₂ = −5 + j2
  1. 1A (−2 − j6)
  2. 2B (−4 + j6)
  3. 3C (4 − j6)
  4. 4D (−6 − j2)
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −3 − j6 and z₂ = −1 + j4, find the real part of w = 2z₁ + 3z₂.

z₁ = −3 − j6z₂ = −1 + j4
Re(w) =
3.Medium
ReIm55−5−5z₁z₂w

Given z₁ = 5∠125° and z₂ = 1.5∠−50°, find the real part of w = z₁·z₂.

z₁ = 5∠125°z₂ = 1.5∠−50°
Re(w) =
4.Medium
ReIm22−2−244−4−4θz

Find the argument θ of z = −5 − j5 in degrees, as the principal value between −180° and 180°.

z = −5 − j5
θ = °
5.Hard
ReIm11−1−122−2−2z₁z₂

Solve z² − 4z + 8 = 0. The roots are a ± jb; find b > 0.

p = −4q = 8
b =
6.Hard
ReIm0.50.5−0.5−0.511−1−1θz

Use De Moivre's theorem to find the real part of z⁴ for z = 1 + j.

z = 1 + jn = 4
Re(z⁴) =

Answer key

  1. 1. D (−6 − j2)
  2. 2. Re(w) = −9
  3. 3. Re(w) = 1.941
  4. 4. θ = −135 °
  5. 5. b = 2
  6. 6. Re(z⁴) = −4

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