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Let z1=10+6i and z2=4+6idot If z is any ...

Let `z_1=10+6i` and `z_2=4+6idot` If `z` is any complex number such that the argument of `((z-z_1))/((z-z_2))` is `pi/4,` then prove that `|z-7-9i|=3sqrt(2)` .

Text Solution

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Since `z_1 = 10 + 6i , z_2 = 4+ 6i`
and arg`((z-z_1)/(z-z_2))-(pi/4)` represente lecue of z is a circle shown as form the figure whose center is (7,y) and `angle AOB = 90^@` clearly OC = 9 `rArr` OD = 6 + 3 =9
`therefore ` Center = (7,9) and readius `= (6)/sqrt(2)=3 sqrt2`

`rArr` Equation of circle is `|z-(7 +9 i )|= 3sqrt(2)`
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