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 = 3 − j7 and z₂ = −3 + j6, find the modulus of the quotient, |z₁/z₂|.

z₁ = 3 − j7z₂ = −3 + j6
|z₁/z₂| =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −4 − j8 and z₂ = 2 + j, find the imaginary part of the product z₁·z₂.

z₁ = −4 − j8z₂ = 2 + j
Im(z₁z₂) =
3.Medium
ReIm22−2−244−4−4θz

Find the argument θ of z = −5 − j in degrees, as the principal value between −180° and 180°.

z = −5 − j
θ = °
4.Medium
ReIm11−1−122−2−233−3−3θz

Write z = 4∠−130° in rectangular form a + jb and give the real part a.

r = 4θ = −130°
a =
5.Hard
ReIm11−1−122−2−2z₀z₁

The roots of zⁿ = w with n = 2 and w = 4∠60° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1. Find the argument of z₀ in degrees, between −180° and 180°.

w = 4∠60°n = 2k = 0
θ₀ = °
6.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 6z + 34 = 0. The roots are a ± jb; find b > 0.

p = 6q = 34
b =

Answer key

  1. 1. |z₁/z₂| = 1.135
  2. 2. Im(z₁z₂) = −20
  3. 3. θ = −168.7 °
  4. 4. a = −2.571
  5. 5. θ₀ = 30 °
  6. 6. b = 5

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