Lecture 1 Complex Numbers - 4unitmaths.com

1. i= Numbers are often denoted asRis the set of real Numbers ,Cis the set of Complex Numbers .Ifzis a complexnumber,zis of the formz=x+iy C,for somex,y 3 + 4iis a Complex +iy real partimaginary +iy,x,y R,therealpartofz= (z) = Re(z)=xtheimaginarypartofz= (z) = Im(z)= +4i (z)=3 (z)= +iy,thenz( zbar ) is given byz=x iyand is called .Ifz=3+4i, thenz=3 2x+3= ( 2) ( 2)2 4(1)(3)2(1)=2 82=2 2 22=1 2i. Lecture 2 Complex 1.(2+3i)+(4+i)=6+ 2.(8 3i) ( 2+4i)=10 1.(2+3i)(1+2i)=2+4i+3i 6= 4+7iExample 2.(3 2i)(3+2i)=9 (2i)2=9+4=13 when we multiply two Complex conjugates, we get a real +3i1+4i=2+3i1+4i 1 4i1 4i=(2+3i)(1 4i)(1+4i)(1 4i)=2 8i+3i 12i21 (4i)2=14 5i17(realisingthe denominator) Lecture , ,ifa+ib=c+idwherea,b,c,d R,thena=candb= ,yif (3 + 4i)2 2(x iy)=x+ hand side (LHS) = 9 16 + 24i 2x+i2y= 7 2x+i(24 + 2y) 7 2x=x3x= 7x= 73&24+2y=yy= 24 Example ,yifx1+i+y2 i=2+ S=x1+i+y2 i=x1+i 1 i1 i+y2 i 2+i2+i=x(1 i)1+1+y(2 +i)4+1=x(1 i)2+y(2 +i)5 Nowx(1 i)2+y(2 +i)5=2+4i.

Lecture 1 Complex Numbers Definitions. Let i2 = −1. ∴ i = −1. Complex numbers are often denoted by z. Just as R is the set of real numbers, C is the set of complex numbers.Ifz is a complex number, z is of the form z = x+ iy ∈ C, for some x,y ∈ R. e.g. 3 + 4i is a complex number. z = x+ iy real part imaginary part.

Loading..

Tags:

  Lecture, Number, Complex, Lecture 1 complex numbers

Information

Related search queries