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
ReIm22−2−244−4−4z₁z₂

For z₁ = 2 − j5 and z₂ = −2 − j3, find the modulus of the product, |z₁z₂|.

z₁ = 2 − j5z₂ = −2 − j3
|z₁z₂| =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 1 + j7 and z₂ = 1 + j, find the imaginary part of the product z₁·z₂.

z₁ = 1 + j7z₂ = 1 + j
Im(z₁z₂) =
3.Medium
ReIm22−2−244−4−4z₁z₂w

Given z₁ = 5∠−35° and z₂ = 3∠65°, find the argument θ of w = z₁/z₂ in degrees, between −180° and 180°.

z₁ = 5∠−35°z₂ = 3∠65°
θ = °
4.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = −1 + j9 in degrees, as the principal value between −180° and 180°.

z = −1 + j9
θ = °
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² − 4z + 20 = 0. The roots are a ± jb; find the real part a.

p = −4q = 20
a =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

Solve z² + 6z + 15.25 = 0. The roots are a ± jb; find b > 0.

p = 6q = 15.25
b =

Answer key

  1. 1. |z₁z₂| = 19.42
  2. 2. Im(z₁z₂) = 8
  3. 3. θ = −100 °
  4. 4. θ = 96.34 °
  5. 5. a = 2
  6. 6. b = 2.5

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