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 − j4, find the imaginary part of w = 2z₁ − 3z̄₂.

z₁ = 6 − j7z₂ = 1 − j4
Im(w) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = 4 − j5 and z₂ = −1 − j4, find the imaginary part of the product z₁·z₂.

z₁ = 4 − j5z₂ = −1 − j4
Im(z₁z₂) =
3.Medium
ReIm22−2−244−4−4θz

Find the argument θ of z = −5 − j4 in degrees, as the principal value between −180° and 180°.

z = −5 − j4
θ = °
4.Medium
ReIm55−5−5θz

Write z = −7 − j7 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = −7 − j7
θ = rad
5.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂z₃

The roots of zⁿ = w with n = 4 and w = 81∠120° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2, 3. Find the imaginary part of z₂.

w = 81∠120°n = 4k = 2
Im(z₂) =
6.Hard
ReIm11−1−122−2−233−3−3θz

Find the real part of (−3 − j2)⁵.

z = −3 − j2n = 5
Re(z⁵) =

Answer key

  1. 1. Im(w) = −26
  2. 2. Im(z₁z₂) = −11
  3. 3. θ = −141.3 °
  4. 4. θ = −2.356 rad
  5. 5. Im(z₂) = −1.5
  6. 6. Re(z⁵) = 597

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