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 = 1 − j8 and z₂ = −2 − j6, find the imaginary part of the quotient z₁/z₂.

z₁ = 1 − j8z₂ = −2 − j6
Im(z₁/z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 8 + j3 and z₂ = 5 + j5, find the imaginary part of the quotient z₁/z₂.

z₁ = 8 + j3z₂ = 5 + j5
Im(z₁/z₂) =
3.Medium
ReIm22−2−244−4−4θz

The number z = 4·ej2.8 has its angle in radians. Find its imaginary part b.

r = 4θ = 2.8 rad
b =
4.Medium
ReIm55−5−51010−10−10θz

Write z = 12∠−75° in rectangular form a + jb and give the imaginary part b.

r = 12θ = −75°
b =
5.Hard
ReIm11−1−122−2−233−3−3z₁z₂

The equation z² − 6z + 15.25 = 0 has two complex roots. Find their modulus |z|.

p = −6q = 15.25
|z| =
6.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z⁴ = 16∠60°. Click it.

w = 16∠60°n = 4
  1. 1A (2∠105°)
  2. 2B (2∠−105°)
  3. 3C (3.6∠150°)
  4. 4D (2∠150°)

Answer key

  1. 1. Im(z₁/z₂) = 0.55
  2. 2. Im(z₁/z₂) = −0.5
  3. 3. b = 1.34
  4. 4. b = −11.59
  5. 5. |z| = 3.905
  6. 6. A (2∠105°)

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