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 − j7 and z₂ = −2 + j5, find the real part of w = −2z₁ + 5z₂.

z₁ = 7 − j7z₂ = −2 + j5
Re(w) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = 4 + j5 and z₂ = −4 − j5, find the modulus of the product, |z₁z₂|.

z₁ = 4 + j5z₂ = −4 − j5
|z₁z₂| =
3.Medium
ReIm22−2−244−4−4θz

Write z = 4∠−155° in rectangular form a + jb and give the real part a.

r = 4θ = −155°
a =
4.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = −5 + j9 in degrees, as the principal value between −180° and 180°.

z = −5 + j9
θ = °
5.Hard
ReIm0.50.5−0.5−0.511−1−11.51.5−1.5−1.5z₁z₂

Solve z² + 3z + 3.25 = 0. The roots are a ± jb; find the real part a.

p = 3q = 3.25
a =
6.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 4z + 20 = 0. The roots are a ± jb; find the real part a.

p = 4q = 20
a =

Answer key

  1. 1. Re(w) = −24
  2. 2. |z₁z₂| = 41
  3. 3. a = −3.625
  4. 4. θ = 119.1 °
  5. 5. a = −1.5
  6. 6. a = −2

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