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
ReIm22−2−244−4−4z₁z₂

For z₁ = −2 − j4 and z₂ = 1 − j2, find the real part of the product z₁·z₂.

z₁ = −2 − j4z₂ = 1 − j2
Re(z₁z₂) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −3 − j5 and z₂ = 3 + j3, find the imaginary part of the product z₁·z₂.

z₁ = −3 − j5z₂ = 3 + j3
Im(z₁z₂) =
3.Medium
ReIm11−1−122−2−233−3−3zABCD

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

z = 1 − jw = 0.5∠−90°
  1. 1A (−2 − j2)
  2. 2B (1 + j)
  3. 3C (2 − j2)
  4. 4D (2 + j2)
4.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = 8 + j9 in degrees, as the principal value between −180° and 180°.

z = 8 + j9
θ = °
5.Hard
ReIm11−1−122−2−2z₁z₂

The equation z² − 3z + 6.25 = 0 has two complex roots. Find their modulus |z|.

p = −3q = 6.25
|z| =
6.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 z₁.

w = 64∠60°n = 3k = 1
Im(z₁) =

Answer key

  1. 1. Re(z₁z₂) = −10
  2. 2. Im(z₁z₂) = −24
  3. 3. D (2 + j2)
  4. 4. θ = 48.37 °
  5. 5. |z| = 2.5
  6. 6. Im(z₁) = 2.571

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