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 = 1 − j5 and z₂ = −2 + j4, find the real part of the quotient z₁/z₂.

z₁ = 1 − j5z₂ = −2 + j4
Re(z₁/z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −8 + j2 and z₂ = 5 + j2, find the real part of w = 4z₁ − 2z̄₂.

z₁ = −8 + j2z₂ = 5 + j2
Re(w) =
3.Medium
ReIm55−5−51010−10−10θz

Write z = 12∠50° in rectangular form a + jb and give the imaginary part b.

r = 12θ = 50°
b =
4.Medium
ReIm55−5−51010−10−10θz

Write z = 12∠−20° in rectangular form a + jb and give the imaginary part b.

r = 12θ = −20°
b =
5.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z³ = 27∠120°. Click it.

w = 27∠120°n = 3
  1. 1A (3∠80°)
  2. 2B (1.5∠−80°)
  3. 3C (3∠−80°)
  4. 4D (3∠−50°)
6.Hard
ReIm11−1−122−2−2z₀z₁z₂z₃z₄

The roots of zⁿ = w with n = 5 and w = 32∠−90° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, …, 4. Find the real part of z₀.

w = 32∠−90°n = 5k = 0
Re(z₀) =

Answer key

  1. 1. Re(z₁/z₂) = −1.1
  2. 2. Re(w) = −42
  3. 3. b = 9.193
  4. 4. b = −4.104
  5. 5. C (3∠−80°)
  6. 6. Re(z₀) = 1.902

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