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 = −8 − j5 and z₂ = 2 + j4, find the imaginary part of the quotient z₁/z₂.

z₁ = −8 − j5z₂ = 2 + j4
Im(z₁/z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 1 + j7 and z₂ = 2 − j3, find the imaginary part of the quotient z₁/z₂.

z₁ = 1 + j7z₂ = 2 − j3
Im(z₁/z₂) =
3.Medium
ReIm55−5−5θz

Find the argument θ of z = 8 + j5 in degrees, as the principal value between −180° and 180°.

z = 8 + j5
θ = °
4.Medium
ReIm0.50.5−0.5−0.511−1−1θz

The number z = 1.5·e−j2.5 has its angle in radians. Find its imaginary part b.

r = 1.5θ = −2.5 rad
b =
5.Hard
ReIm0.50.5−0.5−0.511−1−1z₁z₂

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

p = −2q = 2
a =
6.Hard
ReIm11−1−122−2−2ABCD

Exactly one of the points A–D is a root of z⁴ = 16∠−90°. Click it.

w = 16∠−90°n = 4
  1. 1A (2∠−67.5°)
  2. 2B (2∠112.5°)
  3. 3C (2∠67.5°)
  4. 4D (1∠67.5°)

Answer key

  1. 1. Im(z₁/z₂) = 1.1
  2. 2. Im(z₁/z₂) = 1.308
  3. 3. θ = 32.01 °
  4. 4. b = −0.8977
  5. 5. a = 1
  6. 6. C (2∠67.5°)

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