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 = 6 + j5 and z₂ = 1 + j2, find the modulus of the product, |z₁z₂|.

z₁ = 6 + j5z₂ = 1 + j2
|z₁z₂| =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −1 − j4 and z₂ = −1 − j6, find the imaginary part of the quotient z₁/z₂.

z₁ = −1 − j4z₂ = −1 − j6
Im(z₁/z₂) =
3.Medium
ReIm11−1−122−2−2θz

Write z = 2∠−155° in rectangular form a + jb and give the real part a.

r = 2θ = −155°
a =
4.Medium
ReIm11−1−122−2−2θz

The number z = 3·ej0.8 has its angle in radians. Find its imaginary part b.

r = 3θ = 0.8 rad
b =
5.Hard
ReIm11−1−122−2−2z₀z₁z₂z₃

The roots of zⁿ = w with n = 4 and w = 16∠−60° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2, 3. Find the imaginary part of z₂.

w = 16∠−60°n = 4k = 2
Im(z₂) =
6.Hard
ReIm11−1−122−2−2z₀z₁z₂z₃z₄

The roots of zⁿ = w with n = 5 and w = 32∠45° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, …, 4. Find the imaginary part of z₂.

w = 32∠45°n = 5k = 2
Im(z₂) =

Answer key

  1. 1. |z₁z₂| = 17.46
  2. 2. Im(z₁/z₂) = −0.05405
  3. 3. a = −1.813
  4. 4. b = 2.152
  5. 5. Im(z₂) = 0.5176
  6. 6. Im(z₂) = 0.908

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