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 = −5 + j and z₂ = −5 + j, find the imaginary part of the product z₁·z₂.

z₁ = −5 + jz₂ = −5 + j
Im(z₁z₂) =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = −2 + j4 and z₂ = 6 + j4, find the imaginary part of the product z₁·z₂.

z₁ = −2 + j4z₂ = 6 + j4
Im(z₁z₂) =
3.Medium
ReIm22−2−244−4−466−6−6θz

Write z = −6 + j in exponential form r·ejθ. Give θ in radians, between −π and π.

z = −6 + j
θ = rad
4.Medium
ReIm22−2−244−4−4θz

Write z = −5 + j in exponential form r·ejθ. Give θ in radians, between −π and π.

z = −5 + j
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 real part of z₂.

w = 64∠−90°n = 3k = 2
Re(z₂) =
6.Hard
ReIm22−2−244−4−4z₁z₂

Solve z² − 8z + 17 = 0. The roots are a ± jb; find b > 0.

p = −8q = 17
b =

Answer key

  1. 1. Im(z₁z₂) = −10
  2. 2. Im(z₁z₂) = 16
  3. 3. θ = 2.976 rad
  4. 4. θ = 2.944 rad
  5. 5. Re(z₂) = −3.464
  6. 6. b = 1

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