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 − j7 and z₂ = −1 + j6, find the modulus of the quotient, |z₁/z₂|.

z₁ = 4 − j7z₂ = −1 + j6
|z₁/z₂| =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 4 + j6 and z₂ = 5 + j6, find the real part of the quotient z₁/z₂.

z₁ = 4 + j6z₂ = 5 + j6
Re(z₁/z₂) =
3.Medium
ReIm22−2−244−4−466−6−6z₁z₂w

Given z₁ = 3∠70° and z₂ = 0.5∠−140°, find the real part of w = z₁/z₂.

z₁ = 3∠70°z₂ = 0.5∠−140°
Re(w) =
4.Medium
ReIm0.50.5−0.5−0.511−1−1θz

Find the argument θ of z = 1 + j in degrees, as the principal value between −180° and 180°.

z = 1 + j
θ = °
5.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z³ = 27∠−90°. Click it.

w = 27∠−90°n = 3
  1. 1A (3∠30°)
  2. 2B (3∠−150°)
  3. 3C (3∠150°)
  4. 4D (1.5∠−150°)
6.Hard
ReIm11−1−122−2−2θz

Find the real part of (1 + j2)⁵.

z = 1 + j2n = 5
Re(z⁵) =

Answer key

  1. 1. |z₁/z₂| = 1.325
  2. 2. Re(z₁/z₂) = 0.918
  3. 3. Re(w) = −5.196
  4. 4. θ = 45 °
  5. 5. B (3∠−150°)
  6. 6. Re(z⁵) = 41

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