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 = −2 − j6, find the imaginary part of w = −z₁ + 5z̄₂.

z₁ = −7 − j5z₂ = −2 − j6
Im(w) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −5 + j and z₂ = −2 + j, find the modulus of the product, |z₁z₂|.

z₁ = −5 + jz₂ = −2 + j
|z₁z₂| =
3.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = −9 + j3 in degrees, as the principal value between −180° and 180°.

z = −9 + j3
θ = °
4.Medium
ReIm22−2−244−4−466−6−6z₁z₂w

Given z₁ = 2∠70° and z₂ = 3∠−95°, find the imaginary part of w = z₁·z₂.

z₁ = 2∠70°z₂ = 3∠−95°
Im(w) =
5.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂

The roots of zⁿ = w with n = 3 and w = 27∠60° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2. Find the real part of z₁.

w = 27∠60°n = 3k = 1
Re(z₁) =
6.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂

The roots of zⁿ = w with n = 3 and w = 27∠180° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2. Find the imaginary part of z₂.

w = 27∠180°n = 3k = 2
Im(z₂) =

Answer key

  1. 1. Im(w) = 35
  2. 2. |z₁z₂| = 11.4
  3. 3. θ = 161.6 °
  4. 4. Im(w) = −2.536
  5. 5. Re(z₁) = −2.298
  6. 6. Im(z₂) = −2.598

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