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
ReIm11−1−122−2−233−3−344−4−455−5−566−6−6z₁ABCD

The Argand diagram shows z₁ = −2 − j5. Click the point that represents j·z₁.

z₁ = −2 − j5
  1. 1A (5 + j2)
  2. 2B (−5 + j2)
  3. 3C (5 − j2)
  4. 4D (−5 − j2)
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = 3 + j and z₂ = 4 + j, find the real part of the quotient z₁/z₂.

z₁ = 3 + jz₂ = 4 + j
Re(z₁/z₂) =
3.Medium
ReIm22−2−244−4−466−6−6θz

The number z = 6·ej1.2 has its angle in radians. Find its real part a.

r = 6θ = 1.2 rad
a =
4.Medium
ReIm55−5−5θz

Find the argument θ of z = −8 + j3 in degrees, as the principal value between −180° and 180°.

z = −8 + j3
θ = °
5.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂z₃z₄z₅

The roots of zⁿ = w with n = 6 and w = 729∠45° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, …, 5. Find the imaginary part of z₂.

w = 729∠45°n = 6k = 2
Im(z₂) =
6.Hard
ReIm11−1−122−2−233−3−3z₁z₂

Solve z² − 3z + 11.25 = 0. The roots are a ± jb; find the real part a.

p = −3q = 11.25
a =

Answer key

  1. 1. C (5 − j2)
  2. 2. Re(z₁/z₂) = 0.7647
  3. 3. a = 2.174
  4. 4. θ = 159.4 °
  5. 5. Im(z₂) = 2.38
  6. 6. a = 1.5

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