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 = −5 + j5 and z₂ = −4 + j2, find the real part of the product z₁·z₂.

z₁ = −5 + j5z₂ = −4 + j2
Re(z₁z₂) =
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 −z₁.

z₁ = 4 − j
  1. 1A (−1 + j4)
  2. 2B (4 + j)
  3. 3C (−4 + j)
  4. 4D (1 − j4)
3.Medium
ReIm11−1−122−2−233−3−3z₁z₂w

Given z₁ = 1.5∠−60° and z₂ = 2∠80°, find the real part of w = z₁·z₂.

z₁ = 1.5∠−60°z₂ = 2∠80°
Re(w) =
4.Medium
ReIm11−1−122−2−233−3−3z₁z₂w

Given z₁ = 2∠55° and z₂ = 1.5∠20°, find the argument θ of w = z₁·z₂ in degrees, between −180° and 180°.

z₁ = 2∠55°z₂ = 1.5∠20°
θ = °
5.Hard
ReIm11−1−122−2−2z₁z₂

Solve z² − 5z + 12.5 = 0. The roots are a ± jb; find b > 0.

p = −5q = 12.5
b =
6.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂z₃

The roots of zⁿ = w with n = 4 and w = 81∠180° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2, 3. Find the imaginary part of z₀.

w = 81∠180°n = 4k = 0
Im(z₀) =

Answer key

  1. 1. Re(z₁z₂) = 10
  2. 2. C (−4 + j)
  3. 3. Re(w) = 2.819
  4. 4. θ = 75 °
  5. 5. b = 2.5
  6. 6. Im(z₀) = 2.121

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