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 = −5 − j3, find the real part of the quotient z₁/z₂.

z₁ = −4 + jz₂ = −5 − j3
Re(z₁/z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −3 − j8 and z₂ = 6 + j6, find the real part of the quotient z₁/z₂.

z₁ = −3 − j8z₂ = 6 + j6
Re(z₁/z₂) =
3.Medium
ReIm55−5−5θz

Find the argument θ of z = −2 − j8 in degrees, as the principal value between −180° and 180°.

z = −2 − j8
θ = °
4.Medium
ReIm11−1−122−2−2θz

Write z = 2∠−20° in rectangular form a + jb and give the imaginary part b.

r = 2θ = −20°
b =
5.Hard
ReIm22−2−244−4−4ABCD

Exactly one of the points A–D is a root of z⁴ = 81∠−90°. Click it.

w = 81∠−90°n = 4
  1. 1A (3∠−90°)
  2. 2B (3∠−157.5°)
  3. 3C (3∠157.5°)
  4. 4D (5.4∠−157.5°)
6.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² + 8z + 32 = 0. The roots are a ± jb; find b > 0.

p = 8q = 32
b =

Answer key

  1. 1. Re(z₁/z₂) = 0.5
  2. 2. Re(z₁/z₂) = −0.9167
  3. 3. θ = −104 °
  4. 4. b = −0.684
  5. 5. C (3∠157.5°)
  6. 6. b = 4

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