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# Another P6 Question (Transformations) watch

1. The transformation T from the complex z-plane to the complex w-plane is given by

w = z + 1
. ------
. z + i

show that T maps points on the half-line arg(z) = pi/4 in the z-plane into points on the circle w = l 1 l in the w-plane.

The mark scheme states that:

z = λ + λ i

w = ( λ + 1 ) + λ i
. ----------------
. λ + ( λ + 1 ) i

l ( λ + 1 ) + λ i l = l λ + ( λ + 1 ) i l = √[ ( λ + 1 )² + λ²]

I don't understand the last step, can anyone explain please?

Thanks
2. |x + iy| =√(x² + y²)
|y + ix| = √(y² + x²)
:. |x + iy| = |y + ix| =√(x² + y²)

simply replace x with (λ+1) and y with λ to get the MS explanation
3. arrghh..... thanks very much............

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