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Caption=Multiplication of complex numbers
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Caption=We can treat our euclidean plane as a complex number field.~~Then two-dimensional vectors become complex numbers, ~~vector addition and subtraction - equivalent to complex operations.~~How is the product-vector of the two complex numbers situated?
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Caption=Explore, what is the square of a complex number~~in vector interpretation? When the product of two~~complex numbers is real? When it is equal to (0;-1)?
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Caption=Let us have 2 complex numbers:~~A(a;b) è B(c,d).~~Their product is calculated using formula:~~A*B = (ac-bd) + i(bc+ad)~~~~In our case A([A.X];[A.Y]) and B([B.X];[B.Y]), Ñ = A * B.~~De Moivre's formulas state that:~~~~Arg(AB)=Arg(A)+Arg(B)~~|AB|=|A|*|B|
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Caption=Arg(A) + Arg(B) = [deg(ang(b,o,x)+ang(a,o,x))]°~~Arg(C) = [deg(ang(c,o,x))]°~~~~|A|*|B| = [AO*OB]~~|C| = [OC]
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