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
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −1 − j5 and z₂ = −6 − j2, find the real part of the quotient z₁/z₂.

z₁ = −1 − j5z₂ = −6 − j2
Re(z₁/z₂) =
2.Easy
ReIm11−1−122−2−233−3−3z₁z₂

For z₁ = −1 + j3 and z₂ = 1 + j, find the real part of the product z₁·z₂.

z₁ = −1 + j3z₂ = 1 + j
Re(z₁z₂) =
3.Medium
ReIm11−1−122−2−233−3−3θz

Write z = 4∠−40° in rectangular form a + jb and give the imaginary part b.

r = 4θ = −40°
b =
4.Medium
ReIm55−5−5θz

Find the argument θ of z = −7 − j3 in degrees, as the principal value between −180° and 180°.

z = −7 − j3
θ = °
5.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂z₃

The roots of zⁿ = w with n = 4 and w = 81∠180° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2, 3. Find the real part of z₀.

w = 81∠180°n = 4k = 0
Re(z₀) =
6.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² − 3z + 27.25 = 0. The roots are a ± jb; find b > 0.

p = −3q = 27.25
b =

Answer key

  1. 1. Re(z₁/z₂) = 0.4
  2. 2. Re(z₁z₂) = −4
  3. 3. b = −2.571
  4. 4. θ = −156.8 °
  5. 5. Re(z₀) = 2.121
  6. 6. b = 5

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