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 = −7 + j3 and z₂ = 2 + j, find the imaginary part of the quotient z₁/z₂.

z₁ = −7 + j3z₂ = 2 + j
Im(z₁/z₂) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = 1 − j8 and z₂ = −2 + j3, find the modulus of the quotient, |z₁/z₂|.

z₁ = 1 − j8z₂ = −2 + j3
|z₁/z₂| =
3.Medium
ReIm22−2−244−4−4θz

Find the argument θ of z = −1 − j5 in degrees, as the principal value between −180° and 180°.

z = −1 − j5
θ = °
4.Medium
ReIm22−2−244−4−4θz

Write z = 4∠65° in rectangular form a + jb and give the real part a.

r = 4θ = 65°
a =
5.Hard
ReIm22−2−244−4−4z₀z₁

The roots of zⁿ = w with n = 2 and w = 25∠135° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1. Find the imaginary part of z₁.

w = 25∠135°n = 2k = 1
Im(z₁) =
6.Hard
ReIm11−1−122−2−2θz

Find the real part of (−2 + j)⁴.

z = −2 + jn = 4
Re(z⁴) =

Answer key

  1. 1. Im(z₁/z₂) = 2.6
  2. 2. |z₁/z₂| = 2.236
  3. 3. θ = −101.3 °
  4. 4. a = 1.69
  5. 5. Im(z₁) = −4.619
  6. 6. Re(z⁴) = −7

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