Complex number problem?

mohendra

if |z-4|/|z-8|=1 then what is [Re(z)] ¿

anonymous

Re(z) is the real part of the complex number z.

|z-4|/|z-8|=1

|z-4|=|z-8|

let z = x + yi

|x+ yi - 4| = |x+yi - 8|

|(x-4) + yi| = |(x-8) + yi|

according to the above equation, the modulus of the 2 complex numbers are equal

√{(x-4)^2 + y^2} = √{(x-8)^2 + y^2}

x^2 - 8x + 16 +y^2 = x^2 - 16x + 64 + y^2

-8x +16 = -16x + 64

8x = 48

x = 6

therefore

z = 6 + yi

the real part is 6

so

Re(z) = 6

mecheng2030

z = x + yi => |z| = √(x^2 + y^2) = √((Re(z))^2 + (Im(z))^2)

|z - 4|/|z - 8| = 1

(x - 4)^2 + y^2= (x - 8)^2 + y^2

x^2 - 8x + 16 = x^2 - 16x + 64

8x = 48 => x = 6 = Re(z).