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 + j2 and z₂ = −6 + j4, find the imaginary part of w = 3z₁ + 2z₂.

z₁ = −3 + j2z₂ = −6 + j4
Im(w) =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 6 − j6 and z₂ = 3 + j, find the modulus of the product, |z₁z₂|.

z₁ = 6 − j6z₂ = 3 + j
|z₁z₂| =
3.Medium
ReIm0.50.5−0.5−0.511−1−11.51.5−1.5−1.5θz

The number z = 1.5·ej1.2 has its angle in radians. Find its real part a.

r = 1.5θ = 1.2 rad
a =
4.Medium
ReIm55−5−51010−10−10zABCD

The diagram shows z = 1 + j4. With w = 0.5∠−90°, click the point that represents z/w.

z = 1 + j4w = 0.5∠−90°
  1. 1A (2 + j8)
  2. 2B (−4 + j)
  3. 3C (8 − j2)
  4. 4D (−8 + j2)
5.Hard
ReIm11−1−122−2−2z₁z₂

One root of z³ − 9z² + 25z − 25 = 0 is z₁ = 2 + j. The coefficients are real. Find the real root r.

z₁ = 2 + j
r =
6.Hard
ReIm11−1−122−2−2z₁z₂

One root of z³ − 9z² + 28z − 40 = 0 is z₁ = 2 + j2. The coefficients are real. Find the real root r.

z₁ = 2 + j2
r =

Answer key

  1. 1. Im(w) = 14
  2. 2. |z₁z₂| = 26.83
  3. 3. a = 0.5435
  4. 4. D (−8 + j2)
  5. 5. r = 5
  6. 6. r = 5

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