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 = −6 + j8 and z₂ = 4 − j, find the modulus of the product, |z₁z₂|.

z₁ = −6 + j8z₂ = 4 − j
|z₁z₂| =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 6 − j3 and z₂ = 4 − j6, find the imaginary part of w = −z₁ + 2z₂.

z₁ = 6 − j3z₂ = 4 − j6
Im(w) =
3.Medium
ReIm22−2−244−4−4z₁z₂w

Given z₁ = 3∠150° and z₂ = 1.5∠20°, find the imaginary part of w = z₁·z₂.

z₁ = 3∠150°z₂ = 1.5∠20°
Im(w) =
4.Medium
ReIm55−5−51010−10−10zABCD

The diagram shows z = 2 − j4. With w = 0.5∠−90°, click the point that represents z/w.

z = 2 − j4w = 0.5∠−90°
  1. 1A (2 + j)
  2. 2B (8 + j4)
  3. 3C (4 − j8)
  4. 4D (4 + j2)
5.Hard
ReIm11−1−122−2−2z₀z₁z₂z₃

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

w = 16∠0°n = 4k = 2
Re(z₂) =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

Solve z² − 6z + 18 = 0. The roots are a ± jb; find the real part a.

p = −6q = 18
a =

Answer key

  1. 1. |z₁z₂| = 41.23
  2. 2. Im(w) = −9
  3. 3. Im(w) = 0.7814
  4. 4. B (8 + j4)
  5. 5. Re(z₂) = −2
  6. 6. a = 3

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