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 = 3 − j. Click the point that represents −z₁.

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

For z₁ = 3 + j6 and z₂ = −2 + j5, find the real part of w = 4z₁ + 3z̄₂.

z₁ = 3 + j6z₂ = −2 + j5
Re(w) =
3.Medium
ReIm22−2−244−4−466−6−6z₁z₂w

Given z₁ = 2∠−60° and z₂ = 4∠20°, find the real part of w = z₁·z₂.

z₁ = 2∠−60°z₂ = 4∠20°
Re(w) =
4.Medium
ReIm11−1−122−2−2z₁z₂w

Given z₁ = 2∠150° and z₂ = 0.5∠80°, find the argument θ of w = z₁·z₂ in degrees, between −180° and 180°.

z₁ = 2∠150°z₂ = 0.5∠80°
θ = °
5.Hard
ReIm0.50.5−0.5−0.511−1−1θz

Use De Moivre's theorem to find the real part of z³ for z = 1 − j.

z = 1 − jn = 3
Re(z³) =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

Solve z² + 6z + 15.25 = 0. The roots are a ± jb; find the real part a.

p = 6q = 15.25
a =

Answer key

  1. 1. B (−3 + j)
  2. 2. Re(w) = 6
  3. 3. Re(w) = 6.128
  4. 4. θ = −130 °
  5. 5. Re(z³) = −2
  6. 6. a = −3

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