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UnitB1_ComplexNumber

# UnitB1_ComplexNumber - EE3210 Signal and Systems Unit B1...

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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....
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UnitB1_ComplexNumber - EE3210 Signal and Systems Unit B1...

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