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 − j3 and z₂ = 5 + j2, find the modulus of the product, |z₁z₂|.

z₁ = 8 − j3z₂ = 5 + j2
|z₁z₂| =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −8 − j8 and z₂ = −3 + j5, find the modulus of the product, |z₁z₂|.

z₁ = −8 − j8z₂ = −3 + j5
|z₁z₂| =
3.Medium
ReIm22−2−244−4−4θz

The number z = 5·ej1.2 has its angle in radians. Find its real part a.

r = 5θ = 1.2 rad
a =
4.Medium
ReIm55−5−51010−10−10θz

Write z = 9 − j7 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 9 − j7
θ = rad
5.Hard
ReIm11−1−122−2−2z₁z₂

The equation z² + 5z + 7.25 = 0 has two complex roots. Find their modulus |z|.

p = 5q = 7.25
|z| =
6.Hard
ReIm11−1−122−2−2z₁z₂

Solve z² − 4z + 8 = 0. The roots are a ± jb; find the real part a.

p = −4q = 8
a =

Answer key

  1. 1. |z₁z₂| = 46.01
  2. 2. |z₁z₂| = 65.97
  3. 3. a = 1.812
  4. 4. θ = −0.661 rad
  5. 5. |z| = 2.693
  6. 6. a = 2

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