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
ReIm55−5−5z₁z₂

For z₁ = −5 − j7 and z₂ = −4 + j3, find the imaginary part of the product z₁·z₂.

z₁ = −5 − j7z₂ = −4 + j3
Im(z₁z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 7 + j5 and z₂ = 4 − j4, find the real part of the quotient z₁/z₂.

z₁ = 7 + j5z₂ = 4 − j4
Re(z₁/z₂) =
3.Medium
ReIm22−2−244−4−4θz

Find the argument θ of z = 5 + j3 in degrees, as the principal value between −180° and 180°.

z = 5 + j3
θ = °
4.Medium
ReIm11−1−122−2−233−3−344−4−455−5−5zABCD

The diagram shows z = −1 + j2. With w = 0.5∠90°, click the point that represents z/w.

z = −1 + j2w = 0.5∠90°
  1. 1A (−2 + j4)
  2. 2B (−4 − j2)
  3. 3C (2 + j)
  4. 4D (4 + j2)
5.Hard
ReIm22−2−244−4−4z₀z₁z₂

The roots of zⁿ = w with n = 3 and w = 64∠60° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2. Find the imaginary part of z₂.

w = 64∠60°n = 3k = 2
Im(z₂) =
6.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ − 11z² + 44z − 60 = 0 is z₁ = 4 + j2. The coefficients are real. Find the real root r.

z₁ = 4 + j2
r =

Answer key

  1. 1. Im(z₁z₂) = 13
  2. 2. Re(z₁/z₂) = 0.25
  3. 3. θ = 30.96 °
  4. 4. D (4 + j2)
  5. 5. Im(z₂) = −3.939
  6. 6. r = 3

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