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 − j3 and z₂ = −5 − j5, find the imaginary part of the quotient z₁/z₂.

z₁ = −7 − j3z₂ = −5 − j5
Im(z₁/z₂) =
2.Easy
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−899−9−9z₁z₂ABCD

The Argand diagram shows z₁ = 3 + j2 and z₂ = −4 + j5. Click the point that represents z₁ + z₂.

z₁ = 3 + j2z₂ = −4 + j5
  1. 1A (−1 − j7)
  2. 2B (−7 + j3)
  3. 3C (7 − j)
  4. 4D (−1 + j7)
3.Medium
ReIm22−2−244−4−4z₁z₂w

Given z₁ = 5∠55° and z₂ = 2∠−25°, find the argument θ of w = z₁/z₂ in degrees, between −180° and 180°.

z₁ = 5∠55°z₂ = 2∠−25°
θ = °
4.Medium
ReIm55−5−51010−10−10θz

Write z = 12∠−130° in rectangular form a + jb and give the real part a.

r = 12θ = −130°
a =
5.Hard
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ + z² − 7z + 65 = 0 is z₁ = 2 + j3. The coefficients are real. Find the real root r.

z₁ = 2 + j3
r =
6.Hard
ReIm0.50.5−0.5−0.511−1−1z₁z₂

One root of z³ − 5z² + 8z − 6 = 0 is z₁ = 1 + j. The coefficients are real. Find the real root r.

z₁ = 1 + j
r =

Answer key

  1. 1. Im(z₁/z₂) = −0.4
  2. 2. D (−1 + j7)
  3. 3. θ = 80 °
  4. 4. a = −7.713
  5. 5. r = −5
  6. 6. r = 3

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