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 = −3 + j2 and z₂ = −6 − j4, find the real part of the product z₁·z₂.

z₁ = −3 + j2z₂ = −6 − j4
Re(z₁z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −7 + j5 and z₂ = −4 − j6, find the modulus of the quotient, |z₁/z₂|.

z₁ = −7 + j5z₂ = −4 − j6
|z₁/z₂| =
3.Medium
ReIm55−5−5θz

Write z = 3 − j7 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 3 − j7
θ = rad
4.Medium
ReIm11−1−122−2−233−3−344−4−455−5−5zABCD

The diagram shows z = 2 − j. With w = 0.5∠90°, click the point that represents z/w.

z = 2 − jw = 0.5∠90°
  1. 1A (4 − j2)
  2. 2B (−1 − j2)
  3. 3C (2 + j4)
  4. 4D (−2 − j4)
5.Hard
ReIm22−2−244−4−4z₁z₂

The equation z² − 8z + 25 = 0 has two complex roots. Find their modulus |z|.

p = −8q = 25
|z| =
6.Hard
ReIm0.50.5−0.5−0.511−1−1z₁z₂

One root of z³ − z² + 2 = 0 is z₁ = 1 + j. The coefficients are real. Find the real root r.

z₁ = 1 + j
r =

Answer key

  1. 1. Re(z₁z₂) = 26
  2. 2. |z₁/z₂| = 1.193
  3. 3. θ = −1.166 rad
  4. 4. D (−2 − j4)
  5. 5. |z| = 5
  6. 6. r = −1

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