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 = −3 − j5 and z₂ = −4 − j4, find the imaginary part of w = −2z₁ + 3z₂.

z₁ = −3 − j5z₂ = −4 − j4
Im(w) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −1 + j2 and z₂ = −5 + j4, find the imaginary part of the product z₁·z₂.

z₁ = −1 + j2z₂ = −5 + j4
Im(z₁z₂) =
3.Medium
ReIm11−1−122−2−233−3−3θz

Write z = 3∠160° in rectangular form a + jb and give the real part a.

r = 3θ = 160°
a =
4.Medium
ReIm55−5−5θz

Write z = −3 + j8 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = −3 + j8
θ = rad
5.Hard
ReIm22−2−244−4−4z₀z₁z₂

The roots of zⁿ = w with n = 3 and w = 64∠−90° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2. Find the argument of z₁ in degrees, between −180° and 180°.

w = 64∠−90°n = 3k = 1
θ₁ = °
6.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂z₃z₄

The roots of zⁿ = w with n = 5 and w = 243∠−120° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, …, 4. Find the real part of z₃.

w = 243∠−120°n = 5k = 3
Re(z₃) =

Answer key

  1. 1. Im(w) = −2
  2. 2. Im(z₁z₂) = −14
  3. 3. a = −2.819
  4. 4. θ = 1.93 rad
  5. 5. θ₁ = 90 °
  6. 6. Re(z₃) = −2.934

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