Lecturenotes30March2011

Lecturenotes30March2011 - Section 5.3 Complex Vector...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Section 5.3 Complex Vector Spaces & Appendix B Definition: A complex number is an ordered pair of real numbers, denoted either by ( a,b ) or by a + bi where i = √- 1 . Usual notation is z = a + bi , a=Re(z) is called the real part of z, b=Im(z) is called the imaginary part of z. Set of complex numbers is denoted by C . Definition: Two complex numbers. a + bi and c + di are defined to be equal written as a + bi = c + di if a=c and b=d. Addition, Substraction, Multiplication and Division • Addition: (a+bi)+(c+di)=a+c+(b+d)i • Substraction: (a+bi)-(c+di)=a-c+(b-d)i • Scalar multiplication: k(a+bi)=ka+kbi, k is a real number • Multiplication: (a+bi)(c+di)=(ac-bd)+(ad+bd)i, ( i 2 =- 1 ) Example: Given z 1 = 2- 5 i and z 2 =- 1- i . Find (a) iz 1- z 1 z 2 (b) ( z 1 + 1 + 3 z 2 ) 2 Solution: (a) i(2-5i)-(2-5i)(-1-i)=(2-5i)(i-(-1-i))=(2-5i)(2i+1)=12-i (b) [(2- 5 i ) + 1 + 3(- 1- i )] 2 = [3- 5 i- 3- 3 i ] 2 = (- 8 i ) 2 =- 64 To define division we need Definition: If z=a+bi is any complex number, then the complex conjugate of z is...
View Full Document

This document was uploaded on 04/26/2011.

Page1 / 3

Lecturenotes30March2011 - Section 5.3 Complex Vector...

This preview shows document pages 1 - 2. Sign up to view the full document.

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