Q2Advanced Engineering Mathematics II

Question

Show that the transformation $w = \frac{2 z + 3}{z - 4}$ changes the circle $x^{2} + y^{2} - 4 x = 0$ into the straight lines $4 u + 3 = 0$ .

Answer 1

Question

4 marks

Show that the transformation $w = \frac{2 z + 3}{z - 4}$ changes the circle $x^{2} + y^{2} - 4 x = 0$ into the straight lines $4 u + 3 = 0$ .

Answer

Under w = (2z+3)/(z-4), the circle x^2 + y^2 - 4x = 0 (which passes through z = 4) maps to the straight line 4u + 3 = 0 because z = 4 is a pole mapped to infinity.