1.

The points of intersection of the two curves `|z-3|=2` and `|z|=2` in an argand plane are:

Answer» `Z=x+iy`
`|z|=sqrt(x^2+y^2)=2`
`x^2+y^2=2`
`Z-3=x+iy-3=(x-3)+iy`
`|z-3|=sqrt((x-3)^2+y^2)=2`
`(x-3)^2+y^2=4-(2)`
`cx^2-(x-3)^2=0`
`x^2=(x-3)^2`
`x=pm(x-3)`
`x=x-3`
`x=-x+3`
`2x=3`
`x=3/2`
`y^2=4-9/4`
`y=sqrt7/2`
Intersection=`3/2+sqrt7/2i` and `3/2-sqrt7/2i`
`1/2(3pmisqrt7)`
option 2 is corrrect.


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