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 = −1 + j6 and z₂ = −2 + j6, find the real part of w = 3z₁ − 2z̄₂.

z₁ = −1 + j6z₂ = −2 + j6
Re(w) =
2.Easy
ReIm11−1−122−2−233−3−344−4−455−5−566−6−6z₁ABCD

The Argand diagram shows z₁ = 5 + j. Click the point that represents j·z₁.

z₁ = 5 + j
  1. 1A (−1 + j5)
  2. 2B (−5 − j)
  3. 3C (5 − j)
  4. 4D (−1 − j5)
3.Medium
ReIm55−5−5z₁z₂w

Given z₁ = 5∠125° and z₂ = 1.5∠80°, find the real part of w = z₁·z₂.

z₁ = 5∠125°z₂ = 1.5∠80°
Re(w) =
4.Medium
ReIm55−5−5θz

Find the argument θ of z = −4 − j8 in degrees, as the principal value between −180° and 180°.

z = −4 − j8
θ = °
5.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the imaginary part of z⁷ for z = 1 − j√3.

z = 1 − j√3n = 7
Im(z⁷) =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ − z² − 20z + 50 = 0 is z₁ = 3 + j. The coefficients are real. Find the real root r.

z₁ = 3 + j
r =

Answer key

  1. 1. Re(w) = 1
  2. 2. A (−1 + j5)
  3. 3. Re(w) = −6.797
  4. 4. θ = −116.6 °
  5. 5. Im(z⁷) = −110.9
  6. 6. r = −5

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