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Find the center of the are represented b...

Find the center of the are represented by `a r g[(z-3i)//(z-2i+4)]=pi//4` .

Text Solution

Verified by Experts

If C is the centre of the arc, then `/_BCA = pi//2`

Let C be `z_(c)`. Then,
`(z_(c) - 3i)/(z_(c) - 2i + 4) = e^(ipi//2=i)`
`z_(c) = 3i + i(z_(c) - 2i + 4)`
`therefore z_(c)= (7i + 2)/((1-i))= (1)/(2) (9i - 5)`
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