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>> Geometrical Representation of Fundamental Operations Part-1
Geometrical Representation of Fundamental Operations
(i) Geometrical representation of addition
If two points P and Q represents complex z1 and z2 respectively in the Argard Plane, then the sum z1+z2 is represented by the extremely R of the diagonal OR of parallelogram OPRQ having OP and OQ as two adjacent sides.
(ii) Geometrical representation of subtraction -
(iii) Modules and argument of multiplication of two complex numbers -
Theorem: For any two complex numbers z1, z2
We have, |z1, z2| = |z1| |z2| and arg(z1, z2) = arg(z1) + arg(z2)
Proof: z1 = r1 eiθ, z2 = r2 eiθ2
z1z2 = r1 r2 ei(θ1+θ2)
=> |z1 z2|=|z1|=|z2|
arg (z1z2) = arg(z1) + arg(z2)
i.e., to multiply two complex numbers, we multiply their absolute values and add their arguments.