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 − j and z₂ = −6 − j3, find the modulus of the product, |z₁z₂|.

z₁ = 3 − jz₂ = −6 − j3
|z₁z₂| =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −6 − j8 and z₂ = −1 − j, find the real part of w = −2z₁ − 2z̄₂.

z₁ = −6 − j8z₂ = −1 − j
Re(w) =
3.Medium
ReIm55−5−5θz

Write z = 10∠125° in rectangular form a + jb and give the real part a.

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

The diagram shows z = 4 − j3. With w = 2∠−90°, click the point that represents z·w.

z = 4 − j3w = 2∠−90°
  1. 1A (−6 − j8)
  2. 2B (8 − j6)
  3. 3C (6 + j8)
  4. 4D (−3 − j4)
5.Hard
ReIm22−2−244−4−4ABCD

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

w = 27∠−90°n = 3
  1. 1A (3∠0°)
  2. 2B (3∠30°)
  3. 3C (3∠−30°)
  4. 4D (5.4∠−30°)
6.Hard
ReIm11−1−122−2−2θz

Find the imaginary part of (1 + j2)⁴.

z = 1 + j2n = 4
Im(z⁴) =

Answer key

  1. 1. |z₁z₂| = 21.21
  2. 2. Re(w) = 14
  3. 3. a = −5.736
  4. 4. A (−6 − j8)
  5. 5. C (3∠−30°)
  6. 6. Im(z⁴) = −24

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