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
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 3 + j6 and z₂ = 1 − j, find the real part of the product z₁·z₂.

z₁ = 3 + j6z₂ = 1 − j
Re(z₁z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −8 + j2 and z₂ = −1 + j4, find the real part of w = 4z₁ − 2z̄₂.

z₁ = −8 + j2z₂ = −1 + j4
Re(w) =
3.Medium
ReIm55−5−51010−10−10θz

Write z = 12∠125° in rectangular form a + jb and give the real part a.

r = 12θ = 125°
a =
4.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = −1 + j9 in degrees, as the principal value between −180° and 180°.

z = −1 + j9
θ = °
5.Hard
ReIm22−2−244−4−4ABCD

Exactly one of the points A–D is a root of z⁶ = 64∠90°. Click it.

w = 64∠90°n = 6
  1. 1A (2∠90°)
  2. 2B (2∠45°)
  3. 3C (3.6∠−15°)
  4. 4D (2∠−45°)
6.Hard
ReIm11−1−122−2−2θz

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

z = −√3 + jn = 7
Im(z⁷) =

Answer key

  1. 1. Re(z₁z₂) = 9
  2. 2. Re(w) = −30
  3. 3. a = −6.883
  4. 4. θ = 96.34 °
  5. 5. D (2∠−45°)
  6. 6. Im(z⁷) = −64

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