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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
ReIm55−5−5z₁z₂

For z₁ = 2 + j7 and z₂ = −4 + j, find the real part of the quotient z₁/z₂.

z₁ = 2 + j7z₂ = −4 + j
Re(z₁/z₂) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −1 − j3 and z₂ = 1 − j4, find the real part of w = 2z₁ − 3z̄₂.

z₁ = −1 − j3z₂ = 1 − j4
Re(w) =
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
ReIm11−1−122−2−2θz

Write z = 2.5∠−155° in rectangular form a + jb and give the imaginary part b.

r = 2.5θ = −155°
b =
5.Hard
ReIm11−1−122−2−2z₁z₂

The equation z² + 5z + 12.5 = 0 has two complex roots. Find their modulus |z|.

p = 5q = 12.5
|z| =
6.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂

The roots of zⁿ = w with n = 3 and w = 27∠45° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2. Find the argument of z₂ in degrees, between −180° and 180°.

w = 27∠45°n = 3k = 2
θ₂ = °

Answer key

  1. 1. Re(z₁/z₂) = −0.05882
  2. 2. Re(w) = −5
  3. 3. a = −5.071
  4. 4. b = −1.057
  5. 5. |z| = 3.536
  6. 6. θ₂ = −105 °

Full step-by-step solutions: practise this topic on examproblems.com.