COMPLEX NUMBERS

1
COMPLEX NUMBERS

• . Zx i y gt real (z)x , imag (z)y ,
  i sqrt (-1)
• . z1x1 i y1 , z2x2 i y2
• . Complex conjugate of zx-iy
• . ADD / SUB z1 z2(x1 x2) i (y1 y2)
• . MULT z1.z2(x1iy1)(x2iy2)x1x2-y1y2i(x1y2
  x2y1)
• . DIV z1/z2(x1iy1)/(x2iy2)z1z2/z2.z2
• . CARTESIAN COORDINATE
• . MATLAB real ,imag , complex

2
COMPLEX NUMBERS

• . POLAR COORDINATE representation of complex
  numbers
• . zxiy ? zr. e(i ß) ,
  rsqrt(x2y2) , ßarctan(y/x)
• . xr cos(ß) , yr sin (ß)
• . For conjugate just ß gt - ß
• . z1r1. e(iß1) z2r2 . e(iß2)
• . ADD gt convert to cartesian and add and
  reconvert to polar
• . MULT/DIV multiply or div r1,r2 and add or
  subtract ß1,ß2
• . POWER and ROOT zn(reiß)nr.einß
• . EULER FORMULA
• eiß cos(ß)i
  sin(ß)

3
COMPLEX NUMBERS

• . MATLAB
• ß , r cart2pol ( x , y )
• x , y pol2cart ( ß, r )
• to be continued.