Complex Variables and Partial Differential Equations (3130005)

Question-1c ( i )

BE | Semester-3 Summer-2020 | 27-10-2020

Q1) (c ( i ))

Determine & sketch the image $| z | = 1$ of under the transformation $w = z + i$ .

Let,

w = z + i

\Rightarrow u + iv = (x + iy) + i

\Rightarrow u + iv = x + i (y + 1)

\Rightarrow u = x & v = y + 1

∙ | z | = 1

\Rightarrow \sqrt{x^{2} + y^{2}} = 1 \Rightarrow x^{2} + y^{2} = 1

\Rightarrow u^{2} + {(v - 1)}^{2} = 1

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