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 = −7 + j5 and z₂ = −5 + j, find the real part of the quotient z₁/z₂.

z₁ = −7 + j5z₂ = −5 + j
Re(z₁/z₂) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −5 − j and z₂ = −4 + j2, find the imaginary part of the quotient z₁/z₂.

z₁ = −5 − jz₂ = −4 + j2
Im(z₁/z₂) =
3.Medium
ReIm22−2−244−4−466−6−6θz

Find the argument θ of z = −1 + j6 in degrees, as the principal value between −180° and 180°.

z = −1 + j6
θ = °
4.Medium
ReIm22−2−244−4−4z₁z₂w

Given z₁ = 3∠70° and z₂ = 1.5∠110°, find the argument θ of w = z₁·z₂ in degrees, between −180° and 180°.

z₁ = 3∠70°z₂ = 1.5∠110°
θ = °
5.Hard
ReIm11−1−122−2−2θz

Use De Moivre's theorem to find the imaginary part of z⁸ for z = √3 + j.

z = √3 + jn = 8
Im(z⁸) =
6.Hard
ReIm22−2−244−4−4z₁z₂

The equation z² + 4z + 20 = 0 has two complex roots. Find their modulus |z|.

p = 4q = 20
|z| =

Answer key

  1. 1. Re(z₁/z₂) = 1.538
  2. 2. Im(z₁/z₂) = 0.7
  3. 3. θ = 99.46 °
  4. 4. θ = 180 °
  5. 5. Im(z⁸) = −221.7
  6. 6. |z| = 4.472

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