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
ReIm11−1−122−2−233−3−344−4−455−5−566−6−677−7−788−8−899−9−9z₁z₂ABCD

The Argand diagram shows z₁ = −3 − j4 and z₂ = 4 + j. Click the point that represents z₁ − z₂.

z₁ = −3 − j4z₂ = 4 + j
  1. 1A (−7 + j5)
  2. 2B (−7 − j5)
  3. 3C (−5 − j7)
  4. 4D (7 + j5)
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −5 + j and z₂ = 6 − j5, find the imaginary part of the product z₁·z₂.

z₁ = −5 + jz₂ = 6 − j5
Im(z₁z₂) =
3.Medium
ReIm55−5−51010−10−10zABCD

The diagram shows z = −2 − j4. With w = 0.5∠90°, click the point that represents z/w.

z = −2 − j4w = 0.5∠90°
  1. 1A (−4 − j8)
  2. 2B (−2 + j)
  3. 3C (−8 + j4)
  4. 4D (−4 + j2)
4.Medium
ReIm22−2−244−4−466−6−6θz

Write z = 8∠−130° in rectangular form a + jb and give the real part a.

r = 8θ = −130°
a =
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 6z + 34 = 0. The roots are a ± jb; find the real part a.

p = 6q = 34
a =
6.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z⁴ = 81∠180°. Click it.

w = 81∠180°n = 4
  1. 1A (3∠45°)
  2. 2B (3∠180°)
  3. 3C (3∠90°)
  4. 4D (1.5∠45°)

Answer key

  1. 1. B (−7 − j5)
  2. 2. Im(z₁z₂) = 31
  3. 3. C (−8 + j4)
  4. 4. a = −5.142
  5. 5. a = −3
  6. 6. A (3∠45°)

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