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
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −1 + j and z₂ = −6 + j2, find the real part of the quotient z₁/z₂.

z₁ = −1 + jz₂ = −6 + j2
Re(z₁/z₂) =
2.Easy
ReIm11−1−122−2−233−3−3z₁ABCD

The Argand diagram shows z₁ = 2 − j. Click the point that represents −z₁.

z₁ = 2 − j
  1. 1A (−1 + j2)
  2. 2B (−2 − j)
  3. 3C (−2 + j)
  4. 4D (2 + j)
3.Medium
ReIm11−1−122−2−2θz

The number z = 2·ej2 has its angle in radians. Find its real part a.

r = 2θ = 2 rad
a =
4.Medium
ReIm55−5−51010−10−10zABCD

The diagram shows z = 4 + j. With w = 2∠−90°, click the point that represents z·w.

z = 4 + jw = 2∠−90°
  1. 1A (−2 + j8)
  2. 2B (1 − j4)
  3. 3C (8 + j2)
  4. 4D (2 − j8)
5.Hard
ReIm11−1−122−2−233−3−3θz

Find the real part of (3 − j2)⁵.

z = 3 − j2n = 5
Re(z⁵) =
6.Hard
ReIm11−1−122−2−233−3−3ABCD

Exactly one of the points A–D is a root of z³ = 8∠0°. Click it.

w = 8∠0°n = 3
  1. 1A (2∠−30°)
  2. 2B (2∠30°)
  3. 3C (2∠0°)
  4. 4D (3.6∠60°)

Answer key

  1. 1. Re(z₁/z₂) = 0.2
  2. 2. C (−2 + j)
  3. 3. a = −0.8323
  4. 4. D (2 − j8)
  5. 5. Re(z⁵) = −597
  6. 6. C (2∠0°)

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