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 = −1 − j and z₂ = 5 + j, find the real part of the quotient z₁/z₂.

z₁ = −1 − jz₂ = 5 + j
Re(z₁/z₂) =
2.Easy
ReIm22−2−244−4−4z₁z₂

For z₁ = −2 − j and z₂ = 5 − j, find the real part of the product z₁·z₂.

z₁ = −2 − jz₂ = 5 − j
Re(z₁z₂) =
3.Medium
ReIm55−5−51010−10−10θz

Find the argument θ of z = −9 + j6 in degrees, as the principal value between −180° and 180°.

z = −9 + j6
θ = °
4.Medium
ReIm55−5−51010−10−10θz

Write z = 9 + j in exponential form r·ejθ. Give θ in radians, between −π and π.

z = 9 + j
θ = rad
5.Hard
ReIm11−1−122−2−233−3−3z₁z₂

Solve z² + 5z + 15.25 = 0. The roots are a ± jb; find the real part a.

p = 5q = 15.25
a =
6.Hard
ReIm11−1−122−2−2θz

Find the imaginary part of (1 + j2)⁵.

z = 1 + j2n = 5
Im(z⁵) =

Answer key

  1. 1. Re(z₁/z₂) = −0.2308
  2. 2. Re(z₁z₂) = −11
  3. 3. θ = 146.3 °
  4. 4. θ = 0.1107 rad
  5. 5. a = −2.5
  6. 6. Im(z⁵) = −38

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