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 = −3 − j4 and z₂ = −6 − j6, find the modulus of the product, |z₁z₂|.

z₁ = −3 − j4z₂ = −6 − j6
|z₁z₂| =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = 4 − j2 and z₂ = 2 + j2, find the modulus of the product, |z₁z₂|.

z₁ = 4 − j2z₂ = 2 + j2
|z₁z₂| =
3.Medium
ReIm11−1−122−2−2θz

Write z = 2.5∠−75° in rectangular form a + jb and give the real part a.

r = 2.5θ = −75°
a =
4.Medium
ReIm22−2−244−4−4θz

The number z = 4·ej0.4 has its angle in radians. Find its real part a.

r = 4θ = 0.4 rad
a =
5.Hard
ReIm0.50.5−0.5−0.511−1−1θz

Use De Moivre's theorem to find the real part of z⁷ for z = 1 + j.

z = 1 + jn = 7
Re(z⁷) =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

Solve z² + 2z + 10 = 0. The roots are a ± jb; find b > 0.

p = 2q = 10
b =

Answer key

  1. 1. |z₁z₂| = 42.43
  2. 2. |z₁z₂| = 12.65
  3. 3. a = 0.647
  4. 4. a = 3.684
  5. 5. Re(z⁷) = 8
  6. 6. b = 3

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