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標題:

maths...complexed numbers (transformation)

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發問:

a)Show that the transformation w=(z-1)/z maps |z-1|=1 in the z-plane onto |w|=|w-1| in the w-plane. The region |z-1|=<1 in the z-plane is mapped onto the region T in the w-plane. b) Shade the region T on an Argand diagram.

最佳解答:

a)Show that the transformation w=(z-1)/z maps |z-1|=1 in the z-plane onto |w|=|w-1| in the w-plane. ANSWER w=(z-1)/z wz=z-1 1=z-wz 1=z(1-w) z=1/(1-w) |z-1|=1 becomes |1/(1-w)-1|=1 |[1-(1-w)]/(1-w)|=1 |w/(1-w)|=1 |w|=|w-1| The region |z-1|=<1 in the z-plane is mapped onto the region T in the w-plane. b) Shade the region T on an Argand diagram. ANSWER from (a) |z-1|<=1 becomes |w|<=|w-1| let w=x+yi x^2+y^2<=(x-1)^2+y^2 x^2+y^2<=x^2-2x+1+y^2 2x-1<=0 x<=1/2 So the region T in the w-plane is x<=1/2 你知點畫架啦﹐cheese !

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