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 = 7 − j4 and z₂ = 6 + j3, find the real part of the product z₁·z₂.

z₁ = 7 − j4z₂ = 6 + j3
Re(z₁z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 8 + j8 and z₂ = 2 − j4, find the real part of the product z₁·z₂.

z₁ = 8 + j8z₂ = 2 − j4
Re(z₁z₂) =
3.Medium
ReIm11−1−122−2−233−3−3θz

The number z = 3·e−j1.8 has its angle in radians. Find its imaginary part b.

r = 3θ = −1.8 rad
b =
4.Medium
ReIm22−2−244−4−466−6−6θz

Write z = 8∠35° in rectangular form a + jb and give the real part a.

r = 8θ = 35°
a =
5.Hard
ReIm11−1−122−2−2z₀z₁z₂z₃

The roots of zⁿ = w with n = 4 and w = 16∠180° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2, 3. Find the argument of z₂ in degrees, between −180° and 180°.

w = 16∠180°n = 4k = 2
θ₂ = °
6.Hard
ReIm11−1−122−2−233−3−3z₀z₁

The roots of zⁿ = w with n = 2 and w = 9∠−120° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1. Find the argument of z₁ in degrees, between −180° and 180°.

w = 9∠−120°n = 2k = 1
θ₁ = °

Answer key

  1. 1. Re(z₁z₂) = 54
  2. 2. Re(z₁z₂) = 48
  3. 3. b = −2.922
  4. 4. a = 6.553
  5. 5. θ₂ = −135 °
  6. 6. θ₁ = 120 °

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