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
ReIm55−5−51010−10−101515−15−15z₁z₂ABCD

The Argand diagram shows z₁ = −5 − j5 and z₂ = −2 + j5. Click the point that represents z₁ + z₂.

z₁ = −5 − j5z₂ = −2 + j5
  1. 1A (−3 − j10)
  2. 2B (3 + j10)
  3. 3C (−j7)
  4. 4D (−7)
2.Easy
ReIm11−1−122−2−233−3−344−4−4z₁ABCD

The Argand diagram shows z₁ = −3 + j2. Click the point that represents −z₁.

z₁ = −3 + j2
  1. 1A (3 + j2)
  2. 2B (2 − j3)
  3. 3C (−2 + j3)
  4. 4D (3 − j2)
3.Medium
ReIm11−1−122−2−2θz

The number z = 3·ej2.4 has its angle in radians. Find its imaginary part b.

r = 3θ = 2.4 rad
b =
4.Medium
ReIm22−2−244−4−4z₁z₂w

Given z₁ = 5∠−35° and z₂ = 0.5∠80°, find the imaginary part of w = z₁·z₂.

z₁ = 5∠−35°z₂ = 0.5∠80°
Im(w) =
5.Hard
ReIm22−2−244−4−4z₀z₁

The roots of zⁿ = w with n = 2 and w = 25∠60° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1. Find the real part of z₁.

w = 25∠60°n = 2k = 1
Re(z₁) =
6.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 (3.6∠−150°)
  2. 2B (2∠−120°)
  3. 3C (2∠180°)
  4. 4D (2∠−150°)

Answer key

  1. 1. D (−7)
  2. 2. D (3 − j2)
  3. 3. b = 2.026
  4. 4. Im(w) = 1.768
  5. 5. Re(z₁) = −4.33
  6. 6. D (2∠−150°)

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