(Examples)
(Examples)
Line 13: Line 13:
 
*<math>|1+2j| = \sqrt{5} </math> <br>
 
*<math>|1+2j| = \sqrt{5} </math> <br>
 
*<math>|1-2j| = \sqrt{1^2+(-2)^2} =\sqrt{5}</math>
 
*<math>|1-2j| = \sqrt{1^2+(-2)^2} =\sqrt{5}</math>
 +
*<math>e^{j60} = cos 60 +jsin 60</math>

Revision as of 09:41, 1 September 2008

Definition

  • the complex numbers are combinations of both real parts and imaginary parts, denoted i.
  • These can be written a+bi, where a and b are real numbers.

Some Operations

  • $ j^2 = -1 $
  • $ |a+bj| =\sqrt{a^2+b^2} $
  • $ |z| = |\overline z| $ , where z is complex number
  • Euler Equation : $ e^{aj} = cos a + isin a $

Examples

  • $ |1+2j| = \sqrt{1^2+2^2} $
  • $ |1+2j| = \sqrt{5} $
  • $ |1-2j| = \sqrt{1^2+(-2)^2} =\sqrt{5} $
  • $ e^{j60} = cos 60 +jsin 60 $

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett