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 = −4 − j and z₂ = 1 − j5, find the modulus of the product, |z₁z₂|.

z₁ = −4 − jz₂ = 1 − j5
|z₁z₂| =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −7 + j7 and z₂ = −5 + j2, find the imaginary part of the product z₁·z₂.

z₁ = −7 + j7z₂ = −5 + j2
Im(z₁z₂) =
3.Medium
ReIm11−1−122−2−233−3−344−4−455−5−5zABCD

The diagram shows z = −2 − j. With w = 0.5∠−90°, click the point that represents z/w.

z = −2 − jw = 0.5∠−90°
  1. 1A (2 − j4)
  2. 2B (1 − j2)
  3. 3C (−2 + j4)
  4. 4D (−4 − j2)
4.Medium
ReIm0.50.5−0.5−0.511−1−11.51.5−1.5−1.5z₁z₂w

Given z₁ = 2∠125° and z₂ = 0.5∠−25°, find the imaginary part of w = z₁·z₂.

z₁ = 2∠125°z₂ = 0.5∠−25°
Im(w) =
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 (3.6∠15°)
  2. 2B (2∠−90°)
  3. 3C (2∠−15°)
  4. 4D (2∠15°)
6.Hard
ReIm11−1−122−2−2z₁z₂

Solve z² − 4z + 6.25 = 0. The roots are a ± jb; find the real part a.

p = −4q = 6.25
a =

Answer key

  1. 1. |z₁z₂| = 21.02
  2. 2. Im(z₁z₂) = −49
  3. 3. A (2 − j4)
  4. 4. Im(w) = 0.9848
  5. 5. C (2∠−15°)
  6. 6. a = 2

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