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 = 2 + j2 and z₂ = 5 + j6, find the modulus of the quotient, |z₁/z₂|.

z₁ = 2 + j2z₂ = 5 + j6
|z₁/z₂| =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 4 − j6 and z₂ = −6 + j2, find the modulus of the quotient, |z₁/z₂|.

z₁ = 4 − j6z₂ = −6 + j2
|z₁/z₂| =
3.Medium
ReIm11−1−122−2−2θz

Write z = 2.5∠−20° in rectangular form a + jb and give the imaginary part b.

r = 2.5θ = −20°
b =
4.Medium
ReIm22−2−244−4−4θz

Write z = 4∠65° in rectangular form a + jb and give the real part a.

r = 4θ = 65°
a =
5.Hard
ReIm22−2−244−4−4z₀z₁z₂

The roots of zⁿ = w with n = 3 and w = 64∠60° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2. Find the imaginary part of z₀.

w = 64∠60°n = 3k = 0
Im(z₀) =
6.Hard
ReIm11−1−122−2−2z₁z₂

One root of z³ − 3z² + 4z + 8 = 0 is z₁ = 2 + j2. The coefficients are real. Find the real root r.

z₁ = 2 + j2
r =

Answer key

  1. 1. |z₁/z₂| = 0.3621
  2. 2. |z₁/z₂| = 1.14
  3. 3. b = −0.8551
  4. 4. a = 1.69
  5. 5. Im(z₀) = 1.368
  6. 6. r = −1

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