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
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −4 + j6 and z₂ = −2 + j5, find the real part of w = −2z₁ + 5z̄₂.

z₁ = −4 + j6z₂ = −2 + j5
Re(w) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −3 + j5 and z₂ = −5 − j, find the real part of w = 3z₁ − 2z̄₂.

z₁ = −3 + j5z₂ = −5 − j
Re(w) =
3.Medium
ReIm55−5−5θz

Write z = 10∠50° in rectangular form a + jb and give the imaginary part b.

r = 10θ = 50°
b =
4.Medium
ReIm11−1−122−2−233−3−3z₁z₂w

Given z₁ = 3∠100° and z₂ = 1.5∠45°, find the argument θ of w = z₁/z₂ in degrees, between −180° and 180°.

z₁ = 3∠100°z₂ = 1.5∠45°
θ = °
5.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ − 6z² + 28z − 40 = 0 is z₁ = 2 + j4. The coefficients are real. Find the real root r.

z₁ = 2 + j4
r =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ + 5z² + 7z − 13 = 0 is z₁ = −3 + j2. The coefficients are real. Find the real root r.

z₁ = −3 + j2
r =

Answer key

  1. 1. Re(w) = −2
  2. 2. Re(w) = 1
  3. 3. b = 7.66
  4. 4. θ = 55 °
  5. 5. r = 2
  6. 6. r = 1

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