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 = 6 − j3 and z₂ = 1 + j2, find the real part of w = 3z₁ + 2z̄₂.

z₁ = 6 − j3z₂ = 1 + j2
Re(w) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −5 + j and z₂ = −4 − j3, find the modulus of the product, |z₁z₂|.

z₁ = −5 + jz₂ = −4 − j3
|z₁z₂| =
3.Medium
ReIm11−1−122−2−233−3−344−4−455−5−5zABCD

The diagram shows z = −1 − j2. With w = 2∠90°, click the point that represents z·w.

z = −1 − j2w = 2∠90°
  1. 1A (2 − j)
  2. 2B (−4 + j2)
  3. 3C (4 − j2)
  4. 4D (−2 − j4)
4.Medium
ReIm55−5−5θz

Find the argument θ of z = −7 + j8 in degrees, as the principal value between −180° and 180°.

z = −7 + j8
θ = °
5.Hard
ReIm11−1−122−2−2z₁z₂

One root of z³ − z² − 15z − 25 = 0 is z₁ = −2 + j. The coefficients are real. Find the real root r.

z₁ = −2 + j
r =
6.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ − 6z² + 28z − 40 = 0 is z₁ = 2 + j4. The coefficients are real. Find the real root r.

z₁ = 2 + j4
r =

Answer key

  1. 1. Re(w) = 20
  2. 2. |z₁z₂| = 25.5
  3. 3. C (4 − j2)
  4. 4. θ = 131.2 °
  5. 5. r = 5
  6. 6. r = 2

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