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
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−8z₁z₂ABCD

The Argand diagram shows z₁ = −1 − j5 and z₂ = 2 − j. Click the point that represents z₁ + z₂.

z₁ = −1 − j5z₂ = 2 − j
  1. 1A (3 + j4)
  2. 2B (−3 − j4)
  3. 3C (1 + j6)
  4. 4D (1 − j6)
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −7 + j4 and z₂ = −2 + j6, find the modulus of the product, |z₁z₂|.

z₁ = −7 + j4z₂ = −2 + j6
|z₁z₂| =
3.Medium
ReIm55−5−5θz

Write z = 8 − j3 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 8 − j3
θ = rad
4.Medium
ReIm55−5−5θz

Find the argument θ of z = −8 + j2 in degrees, as the principal value between −180° and 180°.

z = −8 + j2
θ = °
5.Hard
ReIm11−1−122−2−233−3−3θz

Find the imaginary part of (−2 + j3)⁴.

z = −2 + j3n = 4
Im(z⁴) =
6.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 8z + 41 = 0. The roots are a ± jb; find the real part a.

p = 8q = 41
a =

Answer key

  1. 1. D (1 − j6)
  2. 2. |z₁z₂| = 50.99
  3. 3. θ = −0.3588 rad
  4. 4. θ = 166 °
  5. 5. Im(z⁴) = 120
  6. 6. a = −4

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