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
ReIm22−2−244−4−4z₁z₂

For z₁ = −1 − j5 and z₂ = −5 − j, find the imaginary part of the product z₁·z₂.

z₁ = −1 − j5z₂ = −5 − j
Im(z₁z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 7 − j3 and z₂ = −5 + j6, find the real part of the product z₁·z₂.

z₁ = 7 − j3z₂ = −5 + j6
Re(z₁z₂) =
3.Medium
ReIm11−1−122−2−2z₁z₂w

Given z₁ = 1.5∠55° and z₂ = 1.5∠45°, find the imaginary part of w = z₁·z₂.

z₁ = 1.5∠55°z₂ = 1.5∠45°
Im(w) =
4.Medium
ReIm55−5−5θz

Write z = 8∠−75° in rectangular form a + jb and give the real part a.

r = 8θ = −75°
a =
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 (2∠−120°)
  2. 2B (2∠−165°)
  3. 3C (1∠−165°)
  4. 4D (2∠60°)
6.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂

The roots of zⁿ = w with n = 3 and w = 27∠180° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2. Find the imaginary part of z₀.

w = 27∠180°n = 3k = 0
Im(z₀) =

Answer key

  1. 1. Im(z₁z₂) = 26
  2. 2. Re(z₁z₂) = −17
  3. 3. Im(w) = 2.216
  4. 4. a = 2.071
  5. 5. B (2∠−165°)
  6. 6. Im(z₀) = 2.598

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