Chapter 1 - Complex numbers
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| The imaginary unit | i = sqrt(-1)
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| "real" numbers definition | non-imaginary numbers
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| "imaginary" numbers definition | numbers defined only in terms of i
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| complex numbers definition | a number that has real and imaginary parts
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| general form of a complex number | z = a + bi
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| addition of complex numbers | z1 + z2 = a + bi + c + di = (a+ c) + (b + d)i
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| multiplication of complex numbers | z1z2 = (a + bi)(c + di) = ac + (ad + bc)i - bd
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| summation of 2 squares formula | a^2 + b^2 = (a + bi)(a - bi)
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| i^n function | has period 4, i -> -1 -> -i -> 1
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| the complex conjugate of z | if z = a + bi, z* = z - bi
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| complex division | equivilant to realising the denominator, multiply the numerator/denominator by the complex conjugate of the denominator
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| solving for z | let z = a + bi, expand as necessary. Form 2 equations from the real and imaginary parts and solve simutaniously
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| quadratic in terms of its roots | x^2 -(Alpha + Beta)x + (AlphaBeta)
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| sum of the roots of a quadratic | Alpha + Beta = -b/a
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| multiplication of the roots of a quadratic | AlphaBeta = c/a
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| imaginary roots | complex roots of a polynomial with real co-effecients always come in conjugate pairs
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| General roots | Σα = -b/a
Σαβ = c/a
Σαβγ = -d/a
Σαβγδ = e/a
etc
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