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
ReIm55−5−5z₁z₂

For z₁ = 4 + j8 and z₂ = 1 − j6, find the modulus of the quotient, |z₁/z₂|.

z₁ = 4 + j8z₂ = 1 − j6
|z₁/z₂| =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 8 − j3 and z₂ = −3 − j4, find the real part of w = 2z₁ + 5z̄₂.

z₁ = 8 − j3z₂ = −3 − j4
Re(w) =
3.Medium
ReIm0.50.5−0.5−0.511−1−1θz

The number z = 1.5·ej0.6 has its angle in radians. Find its real part a.

r = 1.5θ = 0.6 rad
a =
4.Medium
ReIm55−5−5θz

Write z = 10∠50° in rectangular form a + jb and give the imaginary part b.

r = 10θ = 50°
b =
5.Hard
ReIm22−2−244−4−4ABCD

Exactly one of the points A–D is a root of z⁶ = 729∠60°. Click it.

w = 729∠60°n = 6
  1. 1A (3∠160°)
  2. 2B (3∠−130°)
  3. 3C (3∠130°)
  4. 4D (5.4∠160°)
6.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the imaginary part of z⁷ for z = 1 − j√3.

z = 1 − j√3n = 7
Im(z⁷) =

Answer key

  1. 1. |z₁/z₂| = 1.47
  2. 2. Re(w) = 1
  3. 3. a = 1.238
  4. 4. b = 7.66
  5. 5. C (3∠130°)
  6. 6. Im(z⁷) = −110.9

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