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 = 2 − j3 and z₂ = 5 + j, find the real part of w = −z₁ − 2z̄₂.

z₁ = 2 − j3z₂ = 5 + j
Re(w) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −7 + j and z₂ = 1 − j3, find the imaginary part of the product z₁·z₂.

z₁ = −7 + jz₂ = 1 − j3
Im(z₁z₂) =
3.Medium
ReIm11−1−122−2−2θz

Write z = 2.5∠−40° in rectangular form a + jb and give the real part a.

r = 2.5θ = −40°
a =
4.Medium
ReIm11−1−122−2−233−3−3zABCD

The diagram shows z = 1 − j. With w = 0.5∠90°, click the point that represents z/w.

z = 1 − jw = 0.5∠90°
  1. 1A (2 − j2)
  2. 2B (2 + j2)
  3. 3C (−2 − j2)
  4. 4D (−1 − j)
5.Hard
ReIm11−1−122−2−2ABCD

Exactly one of the points A–D is a root of z³ = 8∠60°. Click it.

w = 8∠60°n = 3
  1. 1A (1∠−100°)
  2. 2B (2∠100°)
  3. 3C (2∠−100°)
  4. 4D (2∠−130°)
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ − 2z² − 6z + 72 = 0 is z₁ = 3 + j3. The coefficients are real. Find the real root r.

z₁ = 3 + j3
r =

Answer key

  1. 1. Re(w) = −12
  2. 2. Im(z₁z₂) = 22
  3. 3. a = 1.915
  4. 4. C (−2 − j2)
  5. 5. C (2∠−100°)
  6. 6. r = −4

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