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
ReIm11−1−122−2−233−3−344−4−455−5−566−6−6z₁ABCD

The Argand diagram shows z₁ = 3 − j5. Click the point that represents −z₁.

z₁ = 3 − j5
  1. 1A (5 − j3)
  2. 2B (−3 + j5)
  3. 3C (−5 + j3)
  4. 4D (3 + j5)
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −1 − j8 and z₂ = 6 + j2, find the real part of the product z₁·z₂.

z₁ = −1 − j8z₂ = 6 + j2
Re(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
ReIm22−2−244−4−4θz

Write z = 5∠110° in rectangular form a + jb and give the real part a.

r = 5θ = 110°
a =
5.Hard
ReIm0.50.5−0.5−0.511−1−1θz

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

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

Exactly one of the points A–D is a root of z³ = 8∠0°. Click it.

w = 8∠0°n = 3
  1. 1A (1∠0°)
  2. 2B (2∠60°)
  3. 3C (2∠30°)
  4. 4D (2∠0°)

Answer key

  1. 1. B (−3 + j5)
  2. 2. Re(z₁z₂) = 10
  3. 3. θ = 110.6 °
  4. 4. a = −1.71
  5. 5. Re(z⁹) = 16
  6. 6. D (2∠0°)

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