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
ReIm55−5−51010−10−10z₁z₂ABCD

The Argand diagram shows z₁ = 5 + j and z₂ = −3 − j3. Click the point that represents z₁ − z₂.

z₁ = 5 + jz₂ = −3 − j3
  1. 1A (8 + j4)
  2. 2B (2 − j2)
  3. 3C (8 − j4)
  4. 4D (−8 − j4)
2.Easy
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−8z₁z₂ABCD

The Argand diagram shows z₁ = −4 − j5 and z₂ = 2 − j. Click the point that represents z₁ + z₂.

z₁ = −4 − j5z₂ = 2 − j
  1. 1A (−2 + j6)
  2. 2B (−2 − j6)
  3. 3C (−6 − j4)
  4. 4D (−6 − j2)
3.Medium
ReIm11−1−122−2−2z₁z₂w

Given z₁ = 2∠125° and z₂ = 1.5∠20°, find the real part of w = z₁·z₂.

z₁ = 2∠125°z₂ = 1.5∠20°
Re(w) =
4.Medium
ReIm0.50.5−0.5−0.511−1−11.51.5−1.5−1.5z₁z₂w

Given z₁ = 2∠−35° and z₂ = 1.5∠−50°, find the real part of w = z₁/z₂.

z₁ = 2∠−35°z₂ = 1.5∠−50°
Re(w) =
5.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z⁶ = 64∠180°. Click it.

w = 64∠180°n = 6
  1. 1A (2∠180°)
  2. 2B (3.6∠−60°)
  3. 3C (2∠−90°)
  4. 4D (2∠−60°)
6.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² − 6z + 34 = 0. The roots are a ± jb; find the real part a.

p = −6q = 34
a =

Answer key

  1. 1. A (8 + j4)
  2. 2. B (−2 − j6)
  3. 3. Re(w) = −2.457
  4. 4. Re(w) = 1.288
  5. 5. C (2∠−90°)
  6. 6. a = 3

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