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 + j3 and z₂ = 5 − j4, find the real part of the product z₁·z₂.

z₁ = 1 + j3z₂ = 5 − j4
Re(z₁z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −8 − j8 and z₂ = −1 − j2, find the real part of the quotient z₁/z₂.

z₁ = −8 − j8z₂ = −1 − j2
Re(z₁/z₂) =
3.Medium
ReIm55−5−5θz

Find the argument θ of z = −3 + j8 in degrees, as the principal value between −180° and 180°.

z = −3 + j8
θ = °
4.Medium
ReIm22−2−244−4−4θz

The number z = 5·ej1.2 has its angle in radians. Find its imaginary part b.

r = 5θ = 1.2 rad
b =
5.Hard
ReIm11−1−122−2−2z₁z₂

One root of z³ − 5z² + 9z − 5 = 0 is z₁ = 2 + j. The coefficients are real. Find the real root r.

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

One root of z³ + 4z² + 14z + 20 = 0 is z₁ = −1 + j3. The coefficients are real. Find the real root r.

z₁ = −1 + j3
r =

Answer key

  1. 1. Re(z₁z₂) = 17
  2. 2. Re(z₁/z₂) = 4.8
  3. 3. θ = 110.6 °
  4. 4. b = 4.66
  5. 5. r = 1
  6. 6. r = −2

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