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 = −6 + j and z₂ = −6 + j4, find the modulus of the product, |z₁z₂|.

z₁ = −6 + jz₂ = −6 + j4
|z₁z₂| =
2.Easy
ReIm11−1−122−2−233−3−344−4−455−5−5z₁ABCD

The Argand diagram shows z₁ = −3 − j4. Click the point that represents z̄₁.

z₁ = −3 − j4
  1. 1A (3 + j4)
  2. 2B (3 − j4)
  3. 3C (−3 + j4)
  4. 4D (−4 − j3)
3.Medium
ReIm55−5−5θz

Write z = 7 − j5 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 7 − j5
θ = rad
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
ReIm11−1−122−2−233−3−3z₁z₂

Solve z² + 6z + 13 = 0. The roots are a ± jb; find the real part a.

p = 6q = 13
a =
6.Hard
ReIm0.50.5−0.5−0.511−1−1θz

Find the imaginary part of (1 + j)³.

z = 1 + jn = 3
Im(z³) =

Answer key

  1. 1. |z₁z₂| = 43.86
  2. 2. C (−3 + j4)
  3. 3. θ = −0.6202 rad
  4. 4. A (6 − j8)
  5. 5. a = −3
  6. 6. Im(z³) = 2

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