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 + j4 and z₂ = −2 + j3, find the modulus of the quotient, |z₁/z₂|.

z₁ = −7 + j4z₂ = −2 + j3
|z₁/z₂| =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −2 + j3 and z₂ = 1 + j4, find the imaginary part of the quotient z₁/z₂.

z₁ = −2 + j3z₂ = 1 + j4
Im(z₁/z₂) =
3.Medium
ReIm22−2−244−4−4θz

The number z = 5·e−j1.8 has its angle in radians. Find its real part a.

r = 5θ = −1.8 rad
a =
4.Medium
ReIm55−5−51010−10−101515−15−15z₁z₂w

Given z₁ = 5∠40° and z₂ = 3∠65°, find the argument θ of w = z₁·z₂ in degrees, between −180° and 180°.

z₁ = 5∠40°z₂ = 3∠65°
θ = °
5.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z³ = 8∠−90°. Click it.

w = 8∠−90°n = 3
  1. 1A (2∠−30°)
  2. 2B (3.6∠30°)
  3. 3C (2∠0°)
  4. 4D (2∠−90°)
6.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z⁴ = 16∠−90°. Click it.

w = 16∠−90°n = 4
  1. 1A (3.6∠−112.5°)
  2. 2B (2∠−67.5°)
  3. 3C (2∠−112.5°)
  4. 4D (2∠112.5°)

Answer key

  1. 1. |z₁/z₂| = 2.236
  2. 2. Im(z₁/z₂) = 0.6471
  3. 3. a = −1.136
  4. 4. θ = 105 °
  5. 5. A (2∠−30°)
  6. 6. C (2∠−112.5°)

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