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 = 7 − j3 and z₂ = 3 − j, find the modulus of the quotient, |z₁/z₂|.

z₁ = 7 − j3z₂ = 3 − j
|z₁/z₂| =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = 3 + j5 and z₂ = −3 + j, find the imaginary part of the quotient z₁/z₂.

z₁ = 3 + j5z₂ = −3 + j
Im(z₁/z₂) =
3.Medium
ReIm11−1−122−2−233−3−3θz

The number z = 3·e−j1.8 has its angle in radians. Find its imaginary part b.

r = 3θ = −1.8 rad
b =
4.Medium
ReIm55−5−5θz

Write z = 8∠−20° in rectangular form a + jb and give the imaginary part b.

r = 8θ = −20°
b =
5.Hard
ReIm11−1−122−2−2ABCD

Exactly one of the points A–D is a root of z⁴ = 16∠60°. Click it.

w = 16∠60°n = 4
  1. 1A (1∠105°)
  2. 2B (2∠105°)
  3. 3C (2∠60°)
  4. 4D (2∠−105°)
6.Hard
ReIm11−1−122−2−2ABCD

Exactly one of the points A–D is a root of z³ = 8∠180°. Click it.

w = 8∠180°n = 3
  1. 1A (2∠30°)
  2. 2B (1∠60°)
  3. 3C (2∠−120°)
  4. 4D (2∠60°)

Answer key

  1. 1. |z₁/z₂| = 2.408
  2. 2. Im(z₁/z₂) = −1.8
  3. 3. b = −2.922
  4. 4. b = −2.736
  5. 5. B (2∠105°)
  6. 6. D (2∠60°)

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