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 = −2 + j2 and z₂ = −5 − j4, find the imaginary part of the product z₁·z₂.

z₁ = −2 + j2z₂ = −5 − j4
Im(z₁z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 8 + j and z₂ = −3 − j4, find the imaginary part of the quotient z₁/z₂.

z₁ = 8 + jz₂ = −3 − j4
Im(z₁/z₂) =
3.Medium
ReIm55−5−5θz

Write z = 7 − j3 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 7 − j3
θ = rad
4.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = −9 − j3 in degrees, as the principal value between −180° and 180°.

z = −9 − j3
θ = °
5.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the real part of z⁴ for z = 1 + j√3.

z = 1 + j√3n = 4
Re(z⁴) =
6.Hard
ReIm22−2−244−4−4z₁z₂

One root of z³ + 13z + 34 = 0 is z₁ = 1 + j4. The coefficients are real. Find the real root r.

z₁ = 1 + j4
r =

Answer key

  1. 1. Im(z₁z₂) = −2
  2. 2. Im(z₁/z₂) = 1.16
  3. 3. θ = −0.4049 rad
  4. 4. θ = −161.6 °
  5. 5. Re(z⁴) = −8
  6. 6. r = −2

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