SE 207: Modeling and Simulation Lesson 3: Review of Complex Analysis

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Presentation transcript:

SE 207: Modeling and Simulation Lesson 3: Review of Complex Analysis Dr. Samir Al-Amer Term 072

Complex Numbers Complex numbers: number of the form z = x + j y where x and y are real numbers and x: real part of z; x = Re {z} y: imaginary part of z; y = Im {z}

Complex Numbers

Representing Complex numbers Rectangular representation Imaginary axis s1=x + j y Imaginary Part y x Real part real axis Complex-plane (s-plane)

Representing Complex numbers Polar representation Imaginary axis Imaginary Part y ρ θ x Real part real axis Complex-plane (s-plane)

Conversion between Representations Example Imaginary axis 4 θ 3 real axis

Euler Formula 4 θ 3

Complex Numbers Addition /Subtraction

Complex Numbers Multiplication/Division

Operations Examples

More Examples

Conjugate Imaginary axis real axis Complex-plane (s-plane)

Conjugate

Conjugate

Conjugate real/imaginary part

Operations Polar coordinate Multiplication/Division

An example

Keywords Conjugate Modulus Real part Imaginary part Polar coordinates Complex plane Imaginary axis Pure imaginary

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