Complex Algebra Review1

Complex Algebra Review1 - Complex Algebra Review Dr. V....

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Complex Algebra Review Dr. V. Këpuska
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2/11/12 Veton Këpuska 2 Complex Algebra Elements u Definitions: u Note: Real numbers can be thought of as complex numbers with imaginary part equal to zero. C R C Ι R then If Numbers Complex all of Set : Numbers Imaginary all of Set : Numbers Real all of Set : 1 number complex a of form Cartezian + = - jy x z x,y j
Background image of page 2
2/11/12 Veton Këpuska 3 Complex Algebra Elements   { } { } z of part Imaginary z of part Real Im Re define then we If 0 If 0 If + = = = = = z y z x jy x z x z y jy z x R I
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2/11/12 Veton Këpuska 4 Euler’s Identity   j e e e e j e j e j e j j j j j j j 2 sin 2 cos sin cos sin cos sin cos θ - - - - = + = - = + = + =
Background image of page 4
2/11/12 Veton Këpuska 5 Polar Form of Complex Numbers u Magnitude of a complex number z is a generalization of the absolute value function/operator  for real numbers. It is buy definition always non-negative. ( 29 z of argument) (or Angle z arg z of Magnitude radians ] , - ( 0 r θ π = = + z r z r re z j R
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2/11/12 Veton Këpuska 6 Polar Form of Complex Numbers u Conversion between polar and rectangular  (Cartesian) forms. u For z=0+j0; called “complex zero” one can not define arg(0+j0).  Why? ( 29 ( 29 [ ] ( 29 ( 29 ( 29 ( 29 = + = = = + = + + = + + = = - x y y x r r y r x jy x jr r jy x j r jy x re z j 1 2 2 tan sin cos sin cos sin cos θ
Background image of page 6
Veton Këpuska 7 Geometric Representation of Complex  Numbers. Q1 Imaginaries
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/10/2012 for the course ECE 3551 taught by Professor Staff during the Spring '11 term at FIT.

Page1 / 24

Complex Algebra Review1 - Complex Algebra Review Dr. V....

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online