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IERG2051 Tutorial 1

IERG2051 Tutorial 1. Kenan Zhou. Outline. Review Complex Numbers Linear Algebra and some mathematics techniques (Use examples in Problem set). What represents a complex number. Typical complex numbers X=a+jb Real part: a Imaginary part: b

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IERG2051 Tutorial 1

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  1. IERG2051 Tutorial 1 Kenan Zhou

  2. Outline • Review Complex Numbers • Linear Algebra and some mathematics techniques (Use examples in Problem set)

  3. What represents a complex number • Typical complex numbers X=a+jb Real part: a Imaginary part: b • Other ways to represent complex numbers X=

  4. Calculation rules of Complex numbers • Simple rules X=a+jb, Y= c+jd Then X+Y=(a+b)+j(c+d) X*Y=(a+jb)*(c+jd)=(ac+jad+jbc-bd) =(ac-bd)+j(ad+bc) if X/Y, then (a+jb)/(c+jd), how to calculate this one?

  5. How to represent a sine wave (sinusoid)? • Complex number notation • a+jbRepresent a vector with a magnitude and phase • Magnitude = • Phase = • Unit vector = jb q a q 1

  6. Rotation: multiplied by j (rotate anti-clockwise) • Period = 2π/w, Frequency = 1/Period = w/2π • Thus we have T=1/f, w=2πf • w : Angular Frequency (i.e. w = 1000 x 2π for a 1000Hz sine wave)

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