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 = −5 − j4 and z₂ = 2 − j4, find the real part of the quotient z₁/z₂.

z₁ = −5 − j4z₂ = 2 − j4
Re(z₁/z₂) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −2 − j4 and z₂ = 2 − j5, find the real part of the product z₁·z₂.

z₁ = −2 − j4z₂ = 2 − j5
Re(z₁z₂) =
3.Medium
ReIm22−2−244−4−4θz

The number z = 5·e−j1.8 has its angle in radians. Find its real part a.

r = 5θ = −1.8 rad
a =
4.Medium
ReIm55−5−5θz

Find the argument θ of z = −8 − j5 in degrees, as the principal value between −180° and 180°.

z = −8 − j5
θ = °
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² − 3z + 27.25 = 0. The roots are a ± jb; find b > 0.

p = −3q = 27.25
b =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

The equation z² − 5z + 15.25 = 0 has two complex roots. Find their modulus |z|.

p = −5q = 15.25
|z| =

Answer key

  1. 1. Re(z₁/z₂) = 0.3
  2. 2. Re(z₁z₂) = −24
  3. 3. a = −1.136
  4. 4. θ = −148 °
  5. 5. b = 5
  6. 6. |z| = 3.905

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