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
ReIm11−1−122−2−233−3−344−4−455−5−566−6−6z₁z₂ABCD

The Argand diagram shows z₁ = −3 − j and z₂ = 2 + j. Click the point that represents z₁ − z₂.

z₁ = −3 − jz₂ = 2 + j
  1. 1A (5 + j2)
  2. 2B (−1)
  3. 3C (−5 − j2)
  4. 4D (−5 + j2)
2.Easy
ReIm55−5−5z₁z₂

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

z₁ = 4 − j8z₂ = −4 − j6
|z₁/z₂| =
3.Medium
ReIm11−1−122−2−233−3−344−4−455−5−5zABCD

The diagram shows z = −2 + j2. With w = 2∠−90°, click the point that represents z·w.

z = −2 + j2w = 2∠−90°
  1. 1A (1 + j)
  2. 2B (2 + j2)
  3. 3C (−4 − j4)
  4. 4D (4 + j4)
4.Medium
ReIm22−2−244−4−4θz

The number z = 4·e−j0.5 has its angle in radians. Find its real part a.

r = 4θ = −0.5 rad
a =
5.Hard
ReIm22−2−244−4−466−6−6ABCD

Exactly one of the points A–D is a root of z⁴ = 81∠60°. Click it.

w = 81∠60°n = 4
  1. 1A (3∠105°)
  2. 2B (3∠150°)
  3. 3C (5.4∠105°)
  4. 4D (3∠60°)
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

Solve z² + 6z + 10 = 0. The roots are a ± jb; find b > 0.

p = 6q = 10
b =

Answer key

  1. 1. C (−5 − j2)
  2. 2. |z₁/z₂| = 1.24
  3. 3. D (4 + j4)
  4. 4. a = 3.51
  5. 5. A (3∠105°)
  6. 6. b = 1

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