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
ReIm55−5−5z₁z₂

For z₁ = 8 − j6 and z₂ = −1 − j2, find the imaginary part of the quotient z₁/z₂.

z₁ = 8 − j6z₂ = −1 − j2
Im(z₁/z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −2 − j8 and z₂ = 1 − j5, find the real part of w = 3z₁ + 5z̄₂.

z₁ = −2 − j8z₂ = 1 − j5
Re(w) =
3.Medium
ReIm55−5−5θz

Write z = 8 − j3 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 8 − j3
θ = rad
4.Medium
ReIm0.50.5−0.5−0.511−1−11.51.5−1.5−1.5θz

Write z = 2∠−130° in rectangular form a + jb and give the imaginary part b.

r = 2θ = −130°
b =
5.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² − 8z + 41 = 0. The roots are a ± jb; find the real part a.

p = −8q = 41
a =
6.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 =

Answer key

  1. 1. Im(z₁/z₂) = 4.4
  2. 2. Re(w) = −1
  3. 3. θ = −0.3588 rad
  4. 4. b = −1.532
  5. 5. a = 4
  6. 6. r = 2

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