lecture1 - Boise State University Department of Electrical...

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

View Full Document Right Arrow Icon
Boise State University Department of Electrical and Computer Engineering ECE212 – Circuit Analysis and Design Lecture #1: The Phasor Transform I Lecture Objectives : 1. To derive and apply Euler’s Identity 2. To derive and apply De Moivre’s Formula 3. To review complex algebra Euler’s Identity : From calculus, e is an irrational number defined as e = lim n →∞ (1 + 1 n ) n = 2 . 718218 . . . n 1 10 100 1000 ··· (1 + 1 /n ) n 2.000000 2.593742 2.704814 2.716924 ··· Expanding e x as a Maclaurin/Taylor series expansion f ( x ) = f (0) + f (0) 1! x + f ′′ (0) 2! x 2 + f ′′′ (0) 3! x 3 + ··· e x = 1 + x 1! + x 2 2! + x 3 3! + x 4 4! + x 5 5! + ··· Example : e 1 = 1 + 1 1! + 1 2 2! + 1 3 3! + 1 4 4! + 1 5 5! | {z } + ··· = 2 . 716667 + ··· Replacing x by the pure imaginary number above yields e = 1 + ( ) + ( ) 2 2! + ( ) 3 3! + ( ) 4 4! + ( ) 5 5! + ··· = (1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

lecture1 - Boise State University Department of Electrical...

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