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 = −3 − j7 and z₂ = −4 − j, find the modulus of the quotient, |z₁/z₂|.

z₁ = −3 − j7z₂ = −4 − j
|z₁/z₂| =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −4 − j6 and z₂ = −6 − j, find the modulus of the quotient, |z₁/z₂|.

z₁ = −4 − j6z₂ = −6 − j
|z₁/z₂| =
3.Medium
ReIm22−2−244−4−466−6−6θz

Write z = 8∠50° in rectangular form a + jb and give the real part a.

r = 8θ = 50°
a =
4.Medium
ReIm55−5−51010−10−10zABCD

The diagram shows z = 1 + j4. With w = 2∠90°, click the point that represents z·w.

z = 1 + j4w = 2∠90°
  1. 1A (−4 + j)
  2. 2B (2 + j8)
  3. 3C (8 − j2)
  4. 4D (−8 + j2)
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 2z + 17 = 0. The roots are a ± jb; find the real part a.

p = 2q = 17
a =
6.Hard
ReIm0.50.5−0.5−0.511−1−1z₁z₂

One root of z³ + 3z² + 4z + 2 = 0 is z₁ = −1 + j. The coefficients are real. Find the real root r.

z₁ = −1 + j
r =

Answer key

  1. 1. |z₁/z₂| = 1.847
  2. 2. |z₁/z₂| = 1.185
  3. 3. a = 5.142
  4. 4. D (−8 + j2)
  5. 5. a = −1
  6. 6. r = −1

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