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 + j8 and z₂ = 4 + j, find the imaginary part of the quotient z₁/z₂.

z₁ = 1 + j8z₂ = 4 + j
Im(z₁/z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −8 − j4 and z₂ = −4 − j3, find the real part of w = −z₁ − 3z₂.

z₁ = −8 − j4z₂ = −4 − j3
Re(w) =
3.Medium
ReIm55−5−51010−10−10z₁z₂w

Given z₁ = 2.5∠100° and z₂ = 4∠20°, find the imaginary part of w = z₁·z₂.

z₁ = 2.5∠100°z₂ = 4∠20°
Im(w) =
4.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = 1 + j9 in degrees, as the principal value between −180° and 180°.

z = 1 + j9
θ = °
5.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ − 5z² + 24z − 20 = 0 is z₁ = 2 + j4. The coefficients are real. Find the real root r.

z₁ = 2 + j4
r =
6.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂z₃z₄

The roots of zⁿ = w with n = 5 and w = 243∠90° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, …, 4. Find the imaginary part of z₁.

w = 243∠90°n = 5k = 1
Im(z₁) =

Answer key

  1. 1. Im(z₁/z₂) = 1.824
  2. 2. Re(w) = 20
  3. 3. Im(w) = 8.66
  4. 4. θ = 83.66 °
  5. 5. r = 1
  6. 6. Im(z₁) = 3

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