If argument of z − z 1 z − z 2 is π 4 ,...
If argument of is , find the locus of .
Approach: I tried to solve the equation using diagram, basically plotting the points on the Argand plane. What I got is a circle with center and a radius of units. The two complex numbers given lie on this circle, and form a chord. Any point lying on the major arc of this chord satisfies the condition.
How exactly would I represent this as a locus of the point? And is there any other method that I can use that does not involve a diagram?
Answer & Explanation
the angle subtended by the chord at the center is so the radius is the center of the chord is you add or subtract so that you will get two centers. the two centres, and form a square of side
Put , so
By the given data, it must be that the real and imaginary parts are identical, and thus
Complete squares, make some algebraic hokus pokus and get a circle.