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 = 8 − j3 and z₂ = 6 − j2, find the modulus of the quotient, |z₁/z₂|.

z₁ = 8 − j3z₂ = 6 − j2
|z₁/z₂| =
2.Easy
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−8z₁z₂ABCD

The Argand diagram shows z₁ = 5 + j2 and z₂ = −1 − j3. Click the point that represents z₁ − z₂.

z₁ = 5 + j2z₂ = −1 − j3
  1. 1A (6 − j5)
  2. 2B (−6 − j5)
  3. 3C (6 + j5)
  4. 4D (5 + j6)
3.Medium
ReIm55−5−5θz

Write z = −1 + j8 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = −1 + j8
θ = rad
4.Medium
ReIm11−1−122−2−233−3−3θz

Write z = 3∠160° in rectangular form a + jb and give the real part a.

r = 3θ = 160°
a =
5.Hard
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ − 9z² + 31z − 39 = 0 is z₁ = 3 + j2. The coefficients are real. Find the real root r.

z₁ = 3 + j2
r =
6.Hard
ReIm11−1−122−2−2z₁z₂

Solve z² − 2z + 5 = 0. The roots are a ± jb; find the real part a.

p = −2q = 5
a =

Answer key

  1. 1. |z₁/z₂| = 1.351
  2. 2. C (6 + j5)
  3. 3. θ = 1.695 rad
  4. 4. a = −2.819
  5. 5. r = 3
  6. 6. a = 1

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