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
ReIm22−2−244−4−4z₁z₂

For z₁ = 2 − j5 and z₂ = 3 + j5, find the modulus of the product, |z₁z₂|.

z₁ = 2 − j5z₂ = 3 + j5
|z₁z₂| =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 8 + j4 and z₂ = −6 + j, find the real part of the product z₁·z₂.

z₁ = 8 + j4z₂ = −6 + j
Re(z₁z₂) =
3.Medium
ReIm22−2−244−4−4θz

Write z = 5∠−115° in rectangular form a + jb and give the imaginary part b.

r = 5θ = −115°
b =
4.Medium
ReIm22−2−244−4−4z₁z₂w

Given z₁ = 1.5∠30° and z₂ = 4∠−95°, find the real part of w = z₁/z₂.

z₁ = 1.5∠30°z₂ = 4∠−95°
Re(w) =
5.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 =
6.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the real part of z⁴ for z = 2 + j2.

z = 2 + j2n = 4
Re(z⁴) =

Answer key

  1. 1. |z₁z₂| = 31.4
  2. 2. Re(z₁z₂) = −52
  3. 3. b = −4.532
  4. 4. Re(w) = −0.2151
  5. 5. b = 3
  6. 6. Re(z⁴) = −64

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