Schultz Hardy
09/27/2024 · Primary School

MATH- 2407 01. Determine the image in the w-plane of the circle \( |\mathbf{z}|=\mathbf{2} \) in the z-plane under the transformation \( \mathbf{w}=\frac{\mathbf{z}+\mathbf{j}}{\mathbf{z}-\mathbf{j}} \) and show the region in the w-plane onto which the region within the circle is mapped.

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The image of the circle \( |\mathbf{z}| = 2 \) under the transformation \( \mathbf{w} = \frac{\mathbf{z} + \mathbf{j}}{\mathbf{z} - \mathbf{j}} \) is a circle in the \( w \)-plane. The specific center and radius of this circle can be determined by evaluating the expressions for \( u \) and \( v \) as \( \theta \) varies from \( 0 \) to \( 2\pi \).

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