Home
Class 12
MATHS
Let P,Q ,R be points represented by comp...

Let P,Q ,R be points represented by complex numbers ` z_(1),z_(2),z_(3)` and circumcentre of ` DeltaPQR` conicides with origin, Let the altitude , PL of the ` Delta` meets the cricumircle again at M, then find the complex number representing the point M.

Text Solution

AI Generated Solution

To find the complex number representing the point \( M \) where the altitude \( PL \) of triangle \( \Delta PQR \) meets the circumcircle again, we can follow these steps: ### Step 1: Understand the Geometry Given points \( P, Q, R \) represented by complex numbers \( z_1, z_2, z_3 \), we know that the circumcenter of triangle \( \Delta PQR \) coincides with the origin. This means that the circumradius is equal for all vertices. ### Step 2: Establish Relationships Since the circumcenter is at the origin, we have: \[ ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|60 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

Similar Questions

Explore conceptually related problems

If the complex numbers z_(1),z_(2),z_(3) are in AP, then they lie on

A,B and C are the points respectively the complex numbers z_(1),z_(2) and z_(3) respectivley, on the complex plane and the circumcentre of /_\ABC lies at the origin. If the altitude of the triangle through the vertex. A meets the circumcircle again at P, prove that P represents the complex number (-(z_(2)z_(3))/(z_(1))) .

If |z|=2, the points representing the complex numbers -1+5z will lie on

If |z|=2, the points representing the complex numbers -1+5z will lie on

If the points represented by complex numbers z_(1)=a+ib, z_(2)=c+id " and " z_(1)-z_(2) are collinear, where i=sqrt(-1) , then

The points representing the complex numbers z for which |z+4|^(2)-|z-4|^(2)=8 lie on

Represent the complex numbers z= 1 + sqrt3i into polar form

Represent the complex number z = 1 +isqrt(3) in the polar form.

The points representing complex number z for which |z+2+ 3i| = 5 lie on the locus given by

Let A,B and C represent the complex number z_1, z_2, z_3 respectively on the complex plane. If the circumcentre of the triangle ABC lies on the origin, then the orthocentre is represented by the number