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
ReIm11−1−122−2−233−3−344−4−455−5−566−6−6z₁ABCD

The Argand diagram shows z₁ = 5 − j2. Click the point that represents j·z₁.

z₁ = 5 − j2
  1. 1A (−5 + j2)
  2. 2B (−2 + j5)
  3. 3C (2 + j5)
  4. 4D (5 + j2)
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = 4 + j2 and z₂ = −3 − j5, find the imaginary part of the quotient z₁/z₂.

z₁ = 4 + j2z₂ = −3 − j5
Im(z₁/z₂) =
3.Medium
ReIm0.50.5−0.5−0.511−1−11.51.5−1.5−1.5z₁z₂w

Given z₁ = 1.5∠30° and z₂ = 1.5∠45°, find the argument θ of w = z₁/z₂ in degrees, between −180° and 180°.

z₁ = 1.5∠30°z₂ = 1.5∠45°
θ = °
4.Medium
ReIm22−2−244−4−4θz

Write z = −4 + j4 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = −4 + j4
θ = rad
5.Hard
ReIm11−1−122−2−233−3−3θz

Find the real part of (3 − j3)⁵.

z = 3 − j3n = 5
Re(z⁵) =
6.Hard
ReIm0.50.5−0.5−0.511−1−1θz

Use De Moivre's theorem to find the imaginary part of z³ for z = −1 + j.

z = −1 + jn = 3
Im(z³) =

Answer key

  1. 1. C (2 + j5)
  2. 2. Im(z₁/z₂) = 0.4118
  3. 3. θ = −15 °
  4. 4. θ = 2.356 rad
  5. 5. Re(z⁵) = −972
  6. 6. Im(z³) = 2

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