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
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 6 + j6 and z₂ = 1 − j4, find the real part of the quotient z₁/z₂.

z₁ = 6 + j6z₂ = 1 − j4
Re(z₁/z₂) =
2.Easy
ReIm11−1−122−2−233−3−344−4−455−5−566−6−6z₁z₂ABCD

The Argand diagram shows z₁ = 3 + j2 and z₂ = 2 − j2. Click the point that represents z₁ − z₂.

z₁ = 3 + j2z₂ = 2 − j2
  1. 1A (1 − j4)
  2. 2B (1 + j4)
  3. 3C (5)
  4. 4D (4 + j)
3.Medium
ReIm22−2−244−4−4θz

Write z = 4∠−115° in rectangular form a + jb and give the imaginary part b.

r = 4θ = −115°
b =
4.Medium
ReIm22−2−244−4−4z₁z₂w

Given z₁ = 4∠30° and z₂ = 0.5∠110°, find the imaginary part of w = z₁·z₂.

z₁ = 4∠30°z₂ = 0.5∠110°
Im(w) =
5.Hard
ReIm0.50.5−0.5−0.511−1−1z₁z₂

The equation z² − 2z + 2 = 0 has two complex roots. Find their modulus |z|.

p = −2q = 2
|z| =
6.Hard
ReIm0.50.5−0.5−0.511−1−1θz

Use De Moivre's theorem to find the real part of z⁴ for z = −1 + j.

z = −1 + jn = 4
Re(z⁴) =

Answer key

  1. 1. Re(z₁/z₂) = −1.059
  2. 2. B (1 + j4)
  3. 3. b = −3.625
  4. 4. Im(w) = 1.286
  5. 5. |z| = 1.414
  6. 6. Re(z⁴) = −4

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