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 + j3. Click the point that represents z̄₁.

z₁ = −5 + j3
  1. 1A (−5 − j3)
  2. 2B (5 + j3)
  3. 3C (−3 + j5)
  4. 4D (3 − j5)
2.Easy
ReIm55−5−51010−10−101515−15−15z₁z₂ABCD

The Argand diagram shows z₁ = 3 − j5 and z₂ = 4 + j4. Click the point that represents z₁ + z₂.

z₁ = 3 − j5z₂ = 4 + j4
  1. 1A (7 + j)
  2. 2B (−1 + j7)
  3. 3C (1 + j9)
  4. 4D (7 − j)
3.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = −9 + j6 in degrees, as the principal value between −180° and 180°.

z = −9 + j6
θ = °
4.Medium
ReIm11−1−122−2−2θz

Write z = 2.5∠35° in rectangular form a + jb and give the real part a.

r = 2.5θ = 35°
a =
5.Hard
ReIm22−2−244−4−4ABCD

Exactly one of the points A–D is a root of z³ = 27∠120°. Click it.

w = 27∠120°n = 3
  1. 1A (3∠160°)
  2. 2B (3∠120°)
  3. 3C (5.4∠−140°)
  4. 4D (3∠−140°)
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. A (−5 − j3)
  2. 2. D (7 − j)
  3. 3. θ = 146.3 °
  4. 4. a = 2.048
  5. 5. A (3∠160°)
  6. 6. r = −4

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