Answer to Question #172220 in Complex Analysis for Rayhan

Question #172220

Let w=f(z)=z^2+6+6i is a complex function. Then the image of the line x=5

 looks like what?


1
Expert's answer
2021-03-17T16:57:24-0400

"w=u+iv=f(z)=(5+iy)^2+6+6i=31-y^2 +i(10y+6)"

"v=10y+6" , hence "y=(v-6)\/10"

"u=31-y^2=31-(v-6)^2\/100"

Therefore the line "x=5" transforms under the function "f(z)" into a parabola with the vertex at (31,6) and the axis "v=6".


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