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 = 5 − j7 and z₂ = −4 + j3, find the imaginary part of the quotient z₁/z₂.

z₁ = 5 − j7z₂ = −4 + j3
Im(z₁/z₂) =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −6 + j and z₂ = −3 − j3, find the modulus of the product, |z₁z₂|.

z₁ = −6 + jz₂ = −3 − j3
|z₁z₂| =
3.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = −9 + j5 in degrees, as the principal value between −180° and 180°.

z = −9 + j5
θ = °
4.Medium
ReIm22−2−244−4−4θz

The number z = 5·ej1.5 has its angle in radians. Find its real part a.

r = 5θ = 1.5 rad
a =
5.Hard
ReIm0.50.5−0.5−0.511−1−11.51.5−1.5−1.5z₁z₂

Solve z² + 2z + 3.25 = 0. The roots are a ± jb; find the real part a.

p = 2q = 3.25
a =
6.Hard
ReIm0.50.5−0.5−0.511−1−1z₁z₂

One root of z³ − 5z² + 8z − 6 = 0 is z₁ = 1 + j. The coefficients are real. Find the real root r.

z₁ = 1 + j
r =

Answer key

  1. 1. Im(z₁/z₂) = 0.52
  2. 2. |z₁z₂| = 25.81
  3. 3. θ = 150.9 °
  4. 4. a = 0.3537
  5. 5. a = −1
  6. 6. r = 3

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