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 = 7 − j7 and z₂ = 2 − j5, find the real part of w = −2z₁ − 3z̄₂.

z₁ = 7 − j7z₂ = 2 − j5
Re(w) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = 5 + j5 and z₂ = −5 − j2, find the imaginary part of the product z₁·z₂.

z₁ = 5 + j5z₂ = −5 − j2
Im(z₁z₂) =
3.Medium
ReIm22−2−244−4−466−6−6θz

Find the argument θ of z = −3 + j6 in degrees, as the principal value between −180° and 180°.

z = −3 + j6
θ = °
4.Medium
ReIm22−2−244−4−4θz

The number z = 4·ej1.2 has its angle in radians. Find its real part a.

r = 4θ = 1.2 rad
a =
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 2z + 26 = 0. The roots are a ± jb; find b > 0.

p = 2q = 26
b =
6.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ − 4z² + 21z − 34 = 0 is z₁ = 1 + j4. The coefficients are real. Find the real root r.

z₁ = 1 + j4
r =

Answer key

  1. 1. Re(w) = −20
  2. 2. Im(z₁z₂) = −35
  3. 3. θ = 116.6 °
  4. 4. a = 1.449
  5. 5. b = 5
  6. 6. r = 2

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