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
ReIm55−5−5z₁z₂

For z₁ = 7 − j5 and z₂ = 1 + j2, find the imaginary part of w = 3z₁ + 2z₂.

z₁ = 7 − j5z₂ = 1 + j2
Im(w) =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 2 + j6 and z₂ = 4 + j2, find the imaginary part of the quotient z₁/z₂.

z₁ = 2 + j6z₂ = 4 + j2
Im(z₁/z₂) =
3.Medium
ReIm55−5−5θz

Find the argument θ of z = −7 + j in degrees, as the principal value between −180° and 180°.

z = −7 + j
θ = °
4.Medium
ReIm11−1−122−2−233−3−3θz

The number z = 3·e−j1.8 has its angle in radians. Find its real part a.

r = 3θ = −1.8 rad
a =
5.Hard
ReIm11−1−122−2−2z₁z₂

One root of z³ + 2z² − 16 = 0 is z₁ = −2 + j2. The coefficients are real. Find the real root r.

z₁ = −2 + j2
r =
6.Hard
ReIm11−1−122−2−233−3−3θz

Find the real part of (−3 − j3)³.

z = −3 − j3n = 3
Re(z³) =

Answer key

  1. 1. Im(w) = −11
  2. 2. Im(z₁/z₂) = 1
  3. 3. θ = 171.9 °
  4. 4. a = −0.6816
  5. 5. r = 2
  6. 6. Re(z³) = 54

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