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 = 3 + j5 and z₂ = 4 + j2, find the imaginary part of the quotient z₁/z₂.

z₁ = 3 + j5z₂ = 4 + j2
Im(z₁/z₂) =
2.Easy
ReIm11−1−122−2−233−3−3z₁ABCD

The Argand diagram shows z₁ = 2 − j. Click the point that represents z̄₁.

z₁ = 2 − j
  1. 1A (−1 + j2)
  2. 2B (−2 + j)
  3. 3C (2 + j)
  4. 4D (−2 − j)
3.Medium
ReIm11−1−122−2−233−3−3θz

The number z = 3·ej2 has its angle in radians. Find its imaginary part b.

r = 3θ = 2 rad
b =
4.Medium
ReIm11−1−122−2−233−3−3z₁z₂w

Given z₁ = 3∠150° and z₂ = 4∠45°, find the argument θ of w = z₁/z₂ in degrees, between −180° and 180°.

z₁ = 3∠150°z₂ = 4∠45°
θ = °
5.Hard
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ + 9z² + 31z + 39 = 0 is z₁ = −3 + j2. The coefficients are real. Find the real root r.

z₁ = −3 + j2
r =
6.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ − 5z² + z + 75 = 0 is z₁ = 4 + j3. The coefficients are real. Find the real root r.

z₁ = 4 + j3
r =

Answer key

  1. 1. Im(z₁/z₂) = 0.7
  2. 2. C (2 + j)
  3. 3. b = 2.728
  4. 4. θ = 105 °
  5. 5. r = −3
  6. 6. r = −3

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