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 = −6 + j4 and z₂ = 4 + j, find the imaginary part of w = 3z₁ + 2z₂.

z₁ = −6 + j4z₂ = 4 + j
Im(w) =
2.Easy
ReIm22−2−244−4−466−6−6z₁z₂

For z₁ = 5 − j6 and z₂ = −6 − j5, find the modulus of the quotient, |z₁/z₂|.

z₁ = 5 − j6z₂ = −6 − j5
|z₁/z₂| =
3.Medium
ReIm11−1−122−2−233−3−3z₁z₂w

Given z₁ = 2∠−35° and z₂ = 0.5∠20°, find the real part of w = z₁/z₂.

z₁ = 2∠−35°z₂ = 0.5∠20°
Re(w) =
4.Medium
ReIm55−5−5θz

Write z = 8 − j3 in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 8 − j3
θ = rad
5.Hard
ReIm11−1−122−2−233−3−3z₁z₂

One root of z³ − 5z² + 16z − 30 = 0 is z₁ = 1 + j3. The coefficients are real. Find the real root r.

z₁ = 1 + j3
r =
6.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂z₃

The roots of zⁿ = w with n = 4 and w = 81∠120° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2, 3. Find the imaginary part of z₃.

w = 81∠120°n = 4k = 3
Im(z₃) =

Answer key

  1. 1. Im(w) = 14
  2. 2. |z₁/z₂| = 1
  3. 3. Re(w) = 2.294
  4. 4. θ = −0.3588 rad
  5. 5. r = 3
  6. 6. Im(z₃) = −2.598

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