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
ReIm55−5−5z₁z₂

For z₁ = −6 + j7 and z₂ = 6 − j4, find the imaginary part of w = 3z₁ − 3z̄₂.

z₁ = −6 + j7z₂ = 6 − j4
Im(w) =
2.Easy
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−899−9−9z₁z₂ABCD

The Argand diagram shows z₁ = 4 + j3 and z₂ = −2 + j4. Click the point that represents z₁ + z₂.

z₁ = 4 + j3z₂ = −2 + j4
  1. 1A (6 − j)
  2. 2B (2 − j7)
  3. 3C (2 + j7)
  4. 4D (−6 + j)
3.Medium
ReIm22−2−244−4−4θz

Find the argument θ of z = −4 − j3 in degrees, as the principal value between −180° and 180°.

z = −4 − j3
θ = °
4.Medium
ReIm11−1−122−2−233−3−3z₁z₂w

Given z₁ = 2.5∠125° and z₂ = 3∠80°, find the real part of w = z₁/z₂.

z₁ = 2.5∠125°z₂ = 3∠80°
Re(w) =
5.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ − 13z² + 65z − 125 = 0 is z₁ = 4 + j3. The coefficients are real. Find the real root r.

z₁ = 4 + j3
r =
6.Hard
ReIm11−1−122−2−2ABCD

Exactly one of the points A–D is a root of z⁴ = 16∠120°. Click it.

w = 16∠120°n = 4
  1. 1A (1∠30°)
  2. 2B (2∠−30°)
  3. 3C (2∠30°)
  4. 4D (2∠75°)

Answer key

  1. 1. Im(w) = 9
  2. 2. C (2 + j7)
  3. 3. θ = −143.1 °
  4. 4. Re(w) = 0.5893
  5. 5. r = 5
  6. 6. C (2∠30°)

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