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 = −6 − j7 and z₂ = 1 − j3, find the imaginary part of w = −z₁ − 2z̄₂.

z₁ = −6 − j7z₂ = 1 − j3
Im(w) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −3 + j5 and z₂ = −5 + j3, find the modulus of the product, |z₁z₂|.

z₁ = −3 + j5z₂ = −5 + j3
|z₁z₂| =
3.Medium
ReIm22−2−244−4−466−6−6θz

The number z = 6·e−j0.5 has its angle in radians. Find its real part a.

r = 6θ = −0.5 rad
a =
4.Medium
ReIm1010−10−102020−20−20z₁z₂w

Given z₁ = 5∠30° and z₂ = 4∠80°, find the argument θ of w = z₁·z₂ in degrees, between −180° and 180°.

z₁ = 5∠30°z₂ = 4∠80°
θ = °
5.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂

The roots of zⁿ = w with n = 3 and w = 27∠90° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2. Find the imaginary part of z₂.

w = 27∠90°n = 3k = 2
Im(z₂) =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

Solve z² + 6z + 10 = 0. The roots are a ± jb; find the real part a.

p = 6q = 10
a =

Answer key

  1. 1. Im(w) = 1
  2. 2. |z₁z₂| = 34
  3. 3. a = 5.265
  4. 4. θ = 110 °
  5. 5. Im(z₂) = −3
  6. 6. a = −3

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