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 = −1 + j5 and z₂ = −1 − j4, find the real part of the quotient z₁/z₂.

z₁ = −1 + j5z₂ = −1 − j4
Re(z₁/z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −8 − j6 and z₂ = −6 + j, find the real part of the quotient z₁/z₂.

z₁ = −8 − j6z₂ = −6 + j
Re(z₁/z₂) =
3.Medium
ReIm55−5−51010−10−10θz

Write z = 12∠−115° in rectangular form a + jb and give the real part a.

r = 12θ = −115°
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
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ − 9z² + 33z − 65 = 0 is z₁ = 2 + j3. The coefficients are real. Find the real root r.

z₁ = 2 + j3
r =
6.Hard
ReIm11−1−122−2−2z₁z₂

The equation z² − 4z + 5 = 0 has two complex roots. Find their modulus |z|.

p = −4q = 5
|z| =

Answer key

  1. 1. Re(z₁/z₂) = −1.118
  2. 2. Re(z₁/z₂) = 1.135
  3. 3. a = −5.071
  4. 4. θ = 119.1 °
  5. 5. r = 5
  6. 6. |z| = 2.236

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