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 −z₁.

z₁ = 4 + j2
  1. 1A (−2 − j4)
  2. 2B (−4 + j2)
  3. 3C (−4 − j2)
  4. 4D (2 + j4)
2.Easy
ReIm11−1−122−2−233−3−344−4−455−5−5z₁ABCD

The Argand diagram shows z₁ = 4 + j. Click the point that represents z̄₁.

z₁ = 4 + j
  1. 1A (−4 − j)
  2. 2B (−1 − j4)
  3. 3C (4 − j)
  4. 4D (1 + j4)
3.Medium
ReIm22−2−244−4−4θz

Write z = 5∠35° in rectangular form a + jb and give the real part a.

r = 5θ = 35°
a =
4.Medium
ReIm55−5−5θz

Find the argument θ of z = −4 + j7 in degrees, as the principal value between −180° and 180°.

z = −4 + j7
θ = °
5.Hard
ReIm11−1−122−2−233−3−3θz

Find the imaginary part of (1 + j3)⁵.

z = 1 + j3n = 5
Im(z⁵) =
6.Hard
ReIm22−2−244−4−4z₁z₂

The equation z² − 8z + 32 = 0 has two complex roots. Find their modulus |z|.

p = −8q = 32
|z| =

Answer key

  1. 1. C (−4 − j2)
  2. 2. C (4 − j)
  3. 3. a = 4.096
  4. 4. θ = 119.7 °
  5. 5. Im(z⁵) = −12
  6. 6. |z| = 5.657

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