The locus of any point `P(z)` on argand plane is `arg((z-5i)/(z+5i))=(pi)/(4)`. Total number of integral points inside the region bounded by the locus

Monjur Alahi

The locus of any point `P(z)` on argand plane is `arg((z-5i)/(z+5i))=(pi)/(4)`.
Total number of integral points inside the region bounded by the locus of `P(z)` and imaginery axis on the argand plane is
A. `62`
B. `74`
C. `136`
D. `138`


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Salim Ahmed Kawsar

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Correct Answer - C
`(c )` Centre `(5,0)`, radius `=5sqrt(2)`
`:.` Equation of the circle `(x-5)^(2)+y^(2)=50`
For `x=1`, `y^(2)=34`.
Total number of integral points `=(5+5+1)`.
Similarly for `x=2,3,…..12`
Finally number of integral points inside the region is `136`.

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