Lecture11

# Lecture11 - OF THE COMPLEX NUMBERS = |z| if give length and...

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cannot find on normal cartesian xy planes exists on diff cartesian 2D system ex. z = 2 - 3i = x + i*y x = 2, y =3 2 = Re(z) while -3 = Im (z)

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can think of complex number as a vector connecting origin to point
work separately with real parts and imaginary parts

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i^2 = -1 because i = sqrt(-1) complex conjugate: z_ = a - i b proof of conjugate link to z+w
15(i)^2 in xy plane - did not have real roots - now we can use imaginary numbers where Q(x) = ax^2 +bx +c not real, complex!

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POLAR REPRESENTATION

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Unformatted text preview: OF THE COMPLEX NUMBERS = |z| if give length and angle - can specify any point z OR if you give x and y | z | = r = sqrt (x^2 + y^2)- the length of the vector is called the modules or absolute value of z- the angle between the positive x real axis and the vector is called the argument of the complex number fi(z)-pi < fi (z) < pi x y find angle - fi = ?- sub in y = 2 y = 4 cos (pi/6) + 4 sin (pi/6) *i GO LOOK BACK AT LINEAR ALGEBRA NOTES TO COMPARE!...
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Lecture11 - OF THE COMPLEX NUMBERS = |z| if give length and...

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