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 = 5 − j2. Click the point that represents z̄₁.

z₁ = 5 − j2
  1. 1A (−2 + j5)
  2. 2B (−5 − j2)
  3. 3C (−5 + j2)
  4. 4D (5 + j2)
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −3 + j8 and z₂ = −1 + j4, find the imaginary part of the product z₁·z₂.

z₁ = −3 + j8z₂ = −1 + j4
Im(z₁z₂) =
3.Medium
ReIm55−5−5θz

Write z = 8∠−20° in rectangular form a + jb and give the real part a.

r = 8θ = −20°
a =
4.Medium
ReIm55−5−5θz

Find the argument θ of z = 8 − j in degrees, as the principal value between −180° and 180°.

z = 8 − j
θ = °
5.Hard
ReIm22−2−244−4−4ABCD

Exactly one of the points A–D is a root of z⁴ = 81∠180°. Click it.

w = 81∠180°n = 4
  1. 1A (3∠90°)
  2. 2B (3∠180°)
  3. 3C (3∠45°)
  4. 4D (5.4∠45°)
6.Hard
ReIm11−1−122−2−2θz

Find the imaginary part of (−1 − j2)⁴.

z = −1 − j2n = 4
Im(z⁴) =

Answer key

  1. 1. D (5 + j2)
  2. 2. Im(z₁z₂) = −20
  3. 3. a = 7.518
  4. 4. θ = −7.125 °
  5. 5. C (3∠45°)
  6. 6. Im(z⁴) = −24

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