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| − | [[Homework 1_ECE301Fall2008mboutin]] [[HW1.1 Allen Humphreys_ECE301Fall2008mboutin| 1.1]] [[HW1.2 Allen Humphreys_ECE301Fall2008mboutin| 1.2]] | + | [[Homework 1_ECE301Fall2008mboutin]] >[[HW1.1 Allen Humphreys_ECE301Fall2008mboutin| 1.1]] >[[HW1.2 Allen Humphreys_ECE301Fall2008mboutin| 1.2]] >1.3 |
==Properties of Complex Number Algebra== | ==Properties of Complex Number Algebra== | ||
Revision as of 18:16, 5 September 2008
Homework 1_ECE301Fall2008mboutin > 1.1 > 1.2 >1.3
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.
