UnitB1_ComplexNumber - EE3210 Signal and Systems Unit B1...

Info iconThis preview shows pages 1–5. 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

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: EE3210 Signal and Systems Unit B1 Complex Numbers EE3210 Signal and Systems: Unit B1 2 What is Complex Number? ♦ Consider the equation x 2 + 1 = 0. ♦ What is its solution? ♦ No solution in the real number system. ♦ Around 1777, the Swiss mathematician Euler introduced the notation ♦ For electrical engineers, i is often used to represent electrical current. To avoid confusion, j is used instead. 1 − = i EE3210 Signal and Systems: Unit B1 3 Cartesian and Polar Form ♦ Cartesian Form: ♦ Polar Form: ♦ Euler’s formula (very important): ♦ r: magnitude of z • (denoted by |z|) ♦ Θ : phase of z θ θ θ j re j r z = + = ) sin (cos a Real Imaginary r b θ θ θ θ sin cos j e j + = bj a z + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = + = = = − a b b a r r b r a 1 2 2 tan , sin , cos θ θ θ z EE3210 Signal and Systems: Unit B1 4 Question Consider X( ω ), a complex function of a real variable ω : a) Express X( ω ) in Cartesian form....
View Full Document

This note was uploaded on 11/22/2009 for the course ELECTRONIC EE3210 taught by Professor Sungchiwan during the Spring '09 term at École Normale Supérieure.

Page1 / 11

UnitB1_ComplexNumber - EE3210 Signal and Systems Unit B1...

This preview shows document pages 1 - 5. Sign up to view the full document.

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