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Geometry of complex numbers watch

    • Thread Starter

    My FP3 syllabus writes the following points:

    (a) carry out operations of multiplication and division of two complex numbers expressed in polar form r(cosθ+isinθ)=r*e, and interpret these operations in geometrical terms;
    (b) understand de Moivre’s theorem, for positive and negative integer exponent, in terms of the geometrical effect of multiplication and division of complex numbers;

    So what does this actually mean? Know (and be able to prove, I suppose) that when you multiply or divide complex numbers, you multiply/divide moduli and add/subtract arguments; the length on an argand diagram is analogous to the modulus; and adding arguments is equivalent to anticlockwise rotation. Is there anything else to it? What does de Moivre's theorem have to do with "the geometrical effect of multiplication and division of complex numbers"?

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