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 + j2 and z₂ = −3 + j5, find the modulus of the product, |z₁z₂|.

z₁ = 6 + j2z₂ = −3 + j5
|z₁z₂| =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −3 + j5 and z₂ = 2 + j, find the real part of the product z₁·z₂.

z₁ = −3 + j5z₂ = 2 + j
Re(z₁z₂) =
3.Medium
ReIm55−5−51010−10−10θz

Write z = −9 + j8 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = −9 + j8
θ = rad
4.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = −9 + j5 in degrees, as the principal value between −180° and 180°.

z = −9 + j5
θ = °
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 5z + 22.25 = 0. The roots are a ± jb; find b > 0.

p = 5q = 22.25
b =
6.Hard
ReIm0.50.5−0.5−0.511−1−1z₁z₂

One root of z³ − 5z² + 8z − 6 = 0 is z₁ = 1 + j. The coefficients are real. Find the real root r.

z₁ = 1 + j
r =

Answer key

  1. 1. |z₁z₂| = 36.88
  2. 2. Re(z₁z₂) = −11
  3. 3. θ = 2.415 rad
  4. 4. θ = 150.9 °
  5. 5. b = 4
  6. 6. r = 3

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