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
ReIm11−1−122−2−233−3−3z₁z₂

For z₁ = 1 + j3 and z₂ = 3 − j, find the imaginary part of w = 3z₁ − 2z̄₂.

z₁ = 1 + j3z₂ = 3 − j
Im(w) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −8 − j and z₂ = 2 − j2, find the real part of the product z₁·z₂.

z₁ = −8 − jz₂ = 2 − j2
Re(z₁z₂) =
3.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 = °
4.Medium
ReIm11−1−122−2−233−3−3θz

The number z = 4·e−j2.5 has its angle in radians. Find its imaginary part b.

r = 4θ = −2.5 rad
b =
5.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the real part of z³ for z = 1 − j√3.

z = 1 − j√3n = 3
Re(z³) =
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. Im(w) = 7
  2. 2. Re(z₁z₂) = −18
  3. 3. θ = 83.66 °
  4. 4. b = −2.394
  5. 5. Re(z³) = −8
  6. 6. r = 2

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