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 = 8 − j2 and z₂ = 6 − j2, find the modulus of the product, |z₁z₂|.

z₁ = 8 − j2z₂ = 6 − j2
|z₁z₂| =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −4 − j and z₂ = 4 + j4, find the real part of the product z₁·z₂.

z₁ = −4 − jz₂ = 4 + j4
Re(z₁z₂) =
3.Medium
ReIm55−5−5θz

Write z = 4 − j8 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 4 − j8
θ = rad
4.Medium
ReIm55−5−51010−10−101515−15−15z₁z₂w

Given z₁ = 5∠−60° and z₂ = 3∠45°, find the real part of w = z₁·z₂.

z₁ = 5∠−60°z₂ = 3∠45°
Re(w) =
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 4z + 29 = 0. The roots are a ± jb; find the real part a.

p = 4q = 29
a =
6.Hard
ReIm22−2−244−4−4z₀z₁z₂

The roots of zⁿ = w with n = 3 and w = 64∠135° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2. Find the real part of z₂.

w = 64∠135°n = 3k = 2
Re(z₂) =

Answer key

  1. 1. |z₁z₂| = 52.15
  2. 2. Re(z₁z₂) = −12
  3. 3. θ = −1.107 rad
  4. 4. Re(w) = 14.49
  5. 5. a = −2
  6. 6. Re(z₂) = 1.035

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