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
ReIm22−2−244−4−4z₁z₂

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

z₁ = 4 + jz₂ = 1 − j4
Im(z₁z₂) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −4 − j2 and z₂ = 1 − j5, find the imaginary part of w = 3z₁ + 3z̄₂.

z₁ = −4 − j2z₂ = 1 − j5
Im(w) =
3.Medium
ReIm22−2−244−4−4θz

Write z = 4∠25° in rectangular form a + jb and give the imaginary part b.

r = 4θ = 25°
b =
4.Medium
ReIm22−2−244−4−4θz

Write z = 5∠35° in rectangular form a + jb and give the real part a.

r = 5θ = 35°
a =
5.Hard
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ + 8z² + 30z + 36 = 0 is z₁ = −3 + j3. The coefficients are real. Find the real root r.

z₁ = −3 + j3
r =
6.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂z₃

The roots of zⁿ = w with n = 4 and w = 81∠90° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2, 3. Find the imaginary part of z₁.

w = 81∠90°n = 4k = 1
Im(z₁) =

Answer key

  1. 1. Im(z₁z₂) = −15
  2. 2. Im(w) = 9
  3. 3. b = 1.69
  4. 4. a = 4.096
  5. 5. r = −2
  6. 6. Im(z₁) = 2.772

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