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 + j and z₂ = −5 + j6, find the real part of w = −2z₁ + 3z̄₂.

z₁ = 8 + jz₂ = −5 + j6
Re(w) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −5 − j3 and z₂ = 3 − j3, find the real part of w = −z₁ − 2z₂.

z₁ = −5 − j3z₂ = 3 − j3
Re(w) =
3.Medium
ReIm22−2−244−4−4θz

Write z = 5∠110° in rectangular form a + jb and give the imaginary part b.

r = 5θ = 110°
b =
4.Medium
ReIm55−5−5θz

Find the argument θ of z = 3 + j8 in degrees, as the principal value between −180° and 180°.

z = 3 + j8
θ = °
5.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the imaginary part of z⁶ for z = −2 − j2.

z = −2 − j2n = 6
Im(z⁶) =
6.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ + 4z² + 13z − 50 = 0 is z₁ = −3 + j4. The coefficients are real. Find the real root r.

z₁ = −3 + j4
r =

Answer key

  1. 1. Re(w) = −31
  2. 2. Re(w) = −1
  3. 3. b = 4.698
  4. 4. θ = 69.44 °
  5. 5. Im(z⁶) = −512
  6. 6. r = 2

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