Activities/Turtle Art/Tutorials/Complex Numbers

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The arithmetic of complex numbers of the form a+bi, for a and b real, is a bit more complicated than real arithmetic, but it is all well within the range of those who have learned elementary algebra in high school. Some of it is within the range of much younger students.

What is a complex number?

A complex number is part of the solution to a number of particular kinds of problem.

  • Quadratic and cubic equations
  • Complex variables
  • Electrical engineering
  • Quantum Mechanics

Addition and subtraction

(a+bi)+(c+di) = (a+c)+(b+d)i

Equivalent to vector addition


1/(a+bi) = (a-bi)/(a-bi)(a+bi) = (a-bi)/(a^2+b^2)