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
ReIm11−1−122−2−233−3−344−4−455−5−5z₁ABCD

The Argand diagram shows z₁ = 4 − j2. Click the point that represents z̄₁.

z₁ = 4 − j2
  1. 1A (−4 + j2)
  2. 2B (−4 − j2)
  3. 3C (2 − j4)
  4. 4D (4 + j2)
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −8 − j4 and z₂ = −5 − j4, find the real part of the product z₁·z₂.

z₁ = −8 − j4z₂ = −5 − j4
Re(z₁z₂) =
3.Medium
ReIm0.50.5−0.5−0.511−1−11.51.5−1.5−1.5θz

The number z = 1.5·ej2 has its angle in radians. Find its imaginary part b.

r = 1.5θ = 2 rad
b =
4.Medium
ReIm55−5−51010−10−10θz

Write z = 12∠125° in rectangular form a + jb and give the imaginary part b.

r = 12θ = 125°
b =
5.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ + 2z² + 12z − 40 = 0 is z₁ = −2 + j4. The coefficients are real. Find the real root r.

z₁ = −2 + j4
r =
6.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 5z + 22.25 = 0. The roots are a ± jb; find the real part a.

p = 5q = 22.25
a =

Answer key

  1. 1. D (4 + j2)
  2. 2. Re(z₁z₂) = 24
  3. 3. b = 1.364
  4. 4. b = 9.83
  5. 5. r = 2
  6. 6. a = −2.5

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