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 = −8 − j4 and z₂ = 5 − j2, find the imaginary part of w = −2z₁ − 2z₂.

z₁ = −8 − j4z₂ = 5 − j2
Im(w) =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 6 − j6 and z₂ = 4 + j5, find the real part of w = 3z₁ − 3z̄₂.

z₁ = 6 − j6z₂ = 4 + j5
Re(w) =
3.Medium
ReIm11−1−122−2−233−3−3θz

Find the argument θ of z = −3 + j3 in degrees, as the principal value between −180° and 180°.

z = −3 + j3
θ = °
4.Medium
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−8zABCD

The diagram shows z = −2 − j3. With w = 0.5∠−90°, click the point that represents z/w.

z = −2 − j3w = 0.5∠−90°
  1. 1A (−6 + j4)
  2. 2B (6 − j4)
  3. 3C (3 − j2)
  4. 4D (−4 − j6)
5.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 =
6.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the real part of z⁴ for z = 2 + j2.

z = 2 + j2n = 4
Re(z⁴) =

Answer key

  1. 1. Im(w) = 12
  2. 2. Re(w) = 6
  3. 3. θ = 135 °
  4. 4. B (6 − j4)
  5. 5. a = −3
  6. 6. Re(z⁴) = −64

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