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 = −7 − j4 and z₂ = −4 + j, find the real part of the product z₁·z₂.

z₁ = −7 − j4z₂ = −4 + j
Re(z₁z₂) =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −2 − j3 and z₂ = −5 + j6, find the imaginary part of the product z₁·z₂.

z₁ = −2 − j3z₂ = −5 + j6
Im(z₁z₂) =
3.Medium
ReIm55−5−5θz

Write z = −7 + j2 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = −7 + j2
θ = rad
4.Medium
ReIm55−5−51010−10−10zABCD

The diagram shows z = −2 + j4. With w = 0.5∠90°, click the point that represents z/w.

z = −2 + j4w = 0.5∠90°
  1. 1A (2 + j)
  2. 2B (−4 + j8)
  3. 3C (8 + j4)
  4. 4D (−8 − j4)
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 8z + 18.25 = 0. The roots are a ± jb; find the real part a.

p = 8q = 18.25
a =
6.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂z₃

The roots of zⁿ = w with n = 4 and w = 81∠0° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2, 3. Find the real part of z₀.

w = 81∠0°n = 4k = 0
Re(z₀) =

Answer key

  1. 1. Re(z₁z₂) = 32
  2. 2. Im(z₁z₂) = 3
  3. 3. θ = 2.863 rad
  4. 4. C (8 + j4)
  5. 5. a = −4
  6. 6. Re(z₀) = 3

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