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

The Argand diagram shows z₁ = −4 − j2. Click the point that represents z̄₁.

z₁ = −4 − j2
  1. 1A (4 + j2)
  2. 2B (−4 + j2)
  3. 3C (−2 − j4)
  4. 4D (2 + j4)
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −8 − j4 and z₂ = −5 − j, find the imaginary part of the product z₁·z₂.

z₁ = −8 − j4z₂ = −5 − j
Im(z₁z₂) =
3.Medium
ReIm22−2−244−4−4θz

Write z = −5 + j2 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = −5 + j2
θ = rad
4.Medium
ReIm11−1−122−2−2z₁z₂w

Given z₁ = 2.5∠125° and z₂ = 2∠−25°, find the argument θ of w = z₁/z₂ in degrees, between −180° and 180°.

z₁ = 2.5∠125°z₂ = 2∠−25°
θ = °
5.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the imaginary part of z⁵ for z = −2 − j2.

z = −2 − j2n = 5
Im(z⁵) =
6.Hard
ReIm11−1−122−2−2ABCD

Exactly one of the points A–D is a root of z⁴ = 16∠90°. Click it.

w = 16∠90°n = 4
  1. 1A (2∠112.5°)
  2. 2B (2∠−112.5°)
  3. 3C (1∠112.5°)
  4. 4D (2∠157.5°)

Answer key

  1. 1. B (−4 + j2)
  2. 2. Im(z₁z₂) = 28
  3. 3. θ = 2.761 rad
  4. 4. θ = 150 °
  5. 5. Im(z⁵) = 128
  6. 6. A (2∠112.5°)

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