Home
Class 11
MATHS
If arg(z-1)=arg(z+3i), then find (x-1):y...

If `arg(z-1)=arg(z+3i)`, then find `(x-1):y`, where `z=x+iy`.

Text Solution

Verified by Experts

Given that, arg `(z - 1) = arg (z + 3i)`
and , let `z = x + iy`
Now, `arg (z -1) = arg(z + 3i)`
`rArr arg (x + iy - 1) = arg (x + iy + 3i)`
`rArr arg (x - 1 + iy) = arg [x + i (y + 3)]`
`rArr tan^(-1).(y)/(x -1) = tan^(-1).(y + 3)/ (x)`
`rArr (y)/(x -1) = (y + 3)/ (x) rArr xy = (x - 1)(y +3)`
` rArr xy = xy - y 3x - 3 rArr 3x - 3 = y`
`rArr (3(x - 1))/(y ) =1 rArr (x - 1)/(y) =(1)/(3)`
`:. (x -1) : y = 1 : 3`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise TRUE/FALSE|9 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|16 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|16 Videos

  • BINOMIAL THEOREM

    NCERT EXEMPLAR|Exercise True/False|7 Videos

  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Objective type|13 Videos

Similar Questions

Explore conceptually related problems

If arg(z-1)=arg(z+2i), then find (x-1):y, where z=x+iy

arg(bar(z))=-arg(z)

If arg(z) lt 0, then find arg(-z) -arg(z) .

If arg (bar (z) _ (1)) = arg (z_ (2)) then

If z= x+iy satisfies the equation arg (z-2)="arg" (2z+3i) , then 3x-4y is equal to

If arg(z_(1))=(2pi)/3 and arg(z_(2))=pi/2 , then find the principal value of arg(z_(1)z_(2)) and also find the quardrant of z_(1)z_(2) .

If z=x+iy and arg((z-2)/(z+2))=(pi)/(6), then find the locus of z.