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 = −6 + j5, find the imaginary part of w = 3z₁ − 2z₂.

z₁ = 7 + j4z₂ = −6 + j5
Im(w) =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −5 − j6 and z₂ = −3 + j3, find the real part of the product z₁·z₂.

z₁ = −5 − j6z₂ = −3 + j3
Re(z₁z₂) =
3.Medium
ReIm55−5−51010−10−10z₁z₂w

Given z₁ = 4∠−60° and z₂ = 3∠45°, find the argument θ of w = z₁·z₂ in degrees, between −180° and 180°.

z₁ = 4∠−60°z₂ = 3∠45°
θ = °
4.Medium
ReIm11−1−122−2−2θz

Write z = 2.5∠65° in rectangular form a + jb and give the imaginary part b.

r = 2.5θ = 65°
b =
5.Hard
ReIm22−2−244−4−4ABCD

Exactly one of the points A–D is a root of z⁴ = 81∠60°. Click it.

w = 81∠60°n = 4
  1. 1A (5.4∠−30°)
  2. 2B (3∠−75°)
  3. 3C (3∠−30°)
  4. 4D (3∠60°)
6.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the imaginary part of z⁷ for z = 2 + j2.

z = 2 + j2n = 7
Im(z⁷) =

Answer key

  1. 1. Im(w) = 2
  2. 2. Re(z₁z₂) = 33
  3. 3. θ = −15 °
  4. 4. b = 2.266
  5. 5. B (3∠−75°)
  6. 6. Im(z⁷) = −1024

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