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
ReIm11−1−122−2−233−3−344−4−4z₁ABCD

The Argand diagram shows z₁ = 1 + j3. Click the point that represents −z₁.

z₁ = 1 + j3
  1. 1A (−1 + j3)
  2. 2B (−3 − j)
  3. 3C (−1 − j3)
  4. 4D (1 − j3)
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 4 − j4 and z₂ = −6 − j3, find the imaginary part of the product z₁·z₂.

z₁ = 4 − j4z₂ = −6 − j3
Im(z₁z₂) =
3.Medium
ReIm55−5−51010−10−10zABCD

The diagram shows z = −4 − j. With w = 0.5∠−90°, click the point that represents z/w.

z = −4 − jw = 0.5∠−90°
  1. 1A (−8 − j2)
  2. 2B (2 − j8)
  3. 3C (1 − j4)
  4. 4D (−2 + j8)
4.Medium
ReIm11−1−122−2−233−3−3z₁z₂w

Given z₁ = 1.5∠30° and z₂ = 0.5∠45°, find the argument θ of w = z₁/z₂ in degrees, between −180° and 180°.

z₁ = 1.5∠30°z₂ = 0.5∠45°
θ = °
5.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ − 9z² + 43z − 75 = 0 is z₁ = 3 + j4. The coefficients are real. Find the real root r.

z₁ = 3 + j4
r =
6.Hard
ReIm0.50.5−0.5−0.511−1−1z₁z₂

One root of z³ + 4z² + 6z + 4 = 0 is z₁ = −1 + j. The coefficients are real. Find the real root r.

z₁ = −1 + j
r =

Answer key

  1. 1. C (−1 − j3)
  2. 2. Im(z₁z₂) = 12
  3. 3. B (2 − j8)
  4. 4. θ = −15 °
  5. 5. r = 3
  6. 6. r = −2

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