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 = −5 + j7 and z₂ = −3 + j3, find the modulus of the quotient, |z₁/z₂|.

z₁ = −5 + j7z₂ = −3 + j3
|z₁/z₂| =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −6 + j3 and z₂ = 5 + j6, find the modulus of the quotient, |z₁/z₂|.

z₁ = −6 + j3z₂ = 5 + j6
|z₁/z₂| =
3.Medium
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−8zABCD

The diagram shows z = 3 + j. With w = 2∠−90°, click the point that represents z·w.

z = 3 + jw = 2∠−90°
  1. 1A (1 − j3)
  2. 2B (−2 + j6)
  3. 3C (6 + j2)
  4. 4D (2 − j6)
4.Medium
ReIm22−2−244−4−4θz

Write z = 4 − j in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 4 − j
θ = rad
5.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z³ = 27∠90°. Click it.

w = 27∠90°n = 3
  1. 1A (3∠−90°)
  2. 2B (3∠90°)
  3. 3C (1.5∠−90°)
  4. 4D (3∠−60°)
6.Hard
ReIm11−1−122−2−2z₁z₂

Solve z² − 5z + 12.5 = 0. The roots are a ± jb; find b > 0.

p = −5q = 12.5
b =

Answer key

  1. 1. |z₁/z₂| = 2.028
  2. 2. |z₁/z₂| = 0.8589
  3. 3. D (2 − j6)
  4. 4. θ = −0.245 rad
  5. 5. A (3∠−90°)
  6. 6. b = 2.5

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