Homework 1_ECE301Fall2008mboutin

> 1.1 > 1.2 > 1.3 > 1.4 > 1.5

Properties of Complex Number Algebra

Complex numbers have certain algebraic properties that are very important when simplifying or solving complex equations.

  • Addition: $ \,(a + bi) + (c + di) = (a + c) + (b + d)i $
  • Subtraction: $ \,(a + bi) - (c + di) = (a - c) + (b - d)i $
  • Multiplication: $ \,(a + bi) (c + di) = ac + bci + adi + bd i^2 = (ac - bd) + (bc + ad)i $
  • Division: $ \,\frac{(a + bi)}{(c + di)} = \left({ac + bd \over c^2 + d^2}\right) + \left( {bc - ad \over c^2 + d^2} \right)i\,, $ where c and d are not both zero.

Alumni Liaison

Prof. Math. Ohio State and Associate Dean
Outstanding Alumnus Purdue Math 2008

Jeff McNeal