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 = 1 − j7 and z₂ = 4 + j4, find the imaginary part of the product z₁·z₂.

z₁ = 1 − j7z₂ = 4 + j4
Im(z₁z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 1 + j7 and z₂ = 4 − j4, find the imaginary part of the quotient z₁/z₂.

z₁ = 1 + j7z₂ = 4 − j4
Im(z₁/z₂) =
3.Medium
ReIm55−5−5θz

Write z = 6 − j8 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 6 − j8
θ = rad
4.Medium
ReIm55−5−51010−10−10zABCD

The diagram shows z = −4 + j3. With w = 0.5∠90°, click the point that represents z/w.

z = −4 + j3w = 0.5∠90°
  1. 1A (−6 − j8)
  2. 2B (−8 + j6)
  3. 3C (3 + j4)
  4. 4D (6 + j8)
5.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ − 7z² + 17z + 25 = 0 is z₁ = 4 + j3. The coefficients are real. Find the real root r.

z₁ = 4 + j3
r =
6.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the real part of z⁶ for z = √3 + j.

z = √3 + jn = 6
Re(z⁶) =

Answer key

  1. 1. Im(z₁z₂) = −24
  2. 2. Im(z₁/z₂) = 1
  3. 3. θ = −0.9273 rad
  4. 4. D (6 + j8)
  5. 5. r = −1
  6. 6. Re(z⁶) = −64

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