prove that image of
the vertical line x=k with k is not =0 to the circle mode of w-1/2k = mode of 1/2k
1
Expert's answer
2020-10-13T18:55:22-0400
z→z1. Hence (x+iy)→x+iy1=x2+y2x−iy . Let u=x2+y2x,v=x2+y2−y. Then (u−2k1)2+v2=u2+v2−ku+4k21=(x2+y2)2x2+y2−ku+4k21=x2+y21−ku+4k21 But here x=k is the given line. Hence u=x2+y2k⇒ku=x2+y21 . Hence RHS= 4k21. Let w=u+iv. Then ∣w−2k1∣=(u−2k1)2+v2=2k.1
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