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
ReIm22−2−244−4−4z₁z₂

For z₁ = −5 + j3 and z₂ = 2 − j4, find the real part of the product z₁·z₂.

z₁ = −5 + j3z₂ = 2 − j4
Re(z₁z₂) =
2.Easy
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−8z₁z₂ABCD

The Argand diagram shows z₁ = −3 − j5 and z₂ = 3 + j. Click the point that represents z₁ + z₂.

z₁ = −3 − j5z₂ = 3 + j
  1. 1A (−j4)
  2. 2B (j4)
  3. 3C (6 + j6)
  4. 4D (−4)
3.Medium
ReIm22−2−244−4−4θz

Find the argument θ of z = 3 − j5 in degrees, as the principal value between −180° and 180°.

z = 3 − j5
θ = °
4.Medium
ReIm22−2−244−4−466−6−6θz

Find the argument θ of z = −6 + j2 in degrees, as the principal value between −180° and 180°.

z = −6 + j2
θ = °
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² − 5z + 31.25 = 0. The roots are a ± jb; find the real part a.

p = −5q = 31.25
a =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ + 2z² + 2z + 40 = 0 is z₁ = 1 + j3. The coefficients are real. Find the real root r.

z₁ = 1 + j3
r =

Answer key

  1. 1. Re(z₁z₂) = 2
  2. 2. A (−j4)
  3. 3. θ = −59.04 °
  4. 4. θ = 161.6 °
  5. 5. a = 2.5
  6. 6. r = −4

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