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
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 5 + j6 and z₂ = −4 − j2, find the real part of the quotient z₁/z₂.

z₁ = 5 + j6z₂ = −4 − j2
Re(z₁/z₂) =
2.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 (3 + j5)
  3. 3C (−5 − j3)
  4. 4D (−5 + j3)
3.Medium
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−8zABCD

The diagram shows z = 3 − j3. With w = 0.5∠90°, click the point that represents z/w.

z = 3 − j3w = 0.5∠90°
  1. 1A (6 + j6)
  2. 2B (−3 − j3)
  3. 3C (−6 − j6)
  4. 4D (6 − j6)
4.Medium
ReIm55−5−5θz

Find the argument θ of z = 6 − j8 in degrees, as the principal value between −180° and 180°.

z = 6 − j8
θ = °
5.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z³ = 27∠60°. Click it.

w = 27∠60°n = 3
  1. 1A (1.5∠140°)
  2. 2B (3∠−40°)
  3. 3C (3∠170°)
  4. 4D (3∠140°)
6.Hard
ReIm11−1−122−2−2z₁z₂

Solve z² − 2z + 7.25 = 0. The roots are a ± jb; find b > 0.

p = −2q = 7.25
b =

Answer key

  1. 1. Re(z₁/z₂) = −1.6
  2. 2. A (5 − j3)
  3. 3. C (−6 − j6)
  4. 4. θ = −53.13 °
  5. 5. D (3∠140°)
  6. 6. b = 2.5

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