## A Little Note on Complex Numbers and Geometry for IITJEE Maths

**Note:**

- In acute triangle, orthocentre (H), centroid (G), and circumcentre (O) are collinear and
- Centroid of the triangle formed by points , , is .
- If the circumcentre of a triangle formed by , and is origin, then its orthocentre is (using 1).

**Example 1: **

Find the relation if , , , are the points of the vertices of a parallelogram taken in order.

**Solution:**

As the diagonals of a parallelogram bisect each other, the affix of the mid-point of AC is same as the affix of the mid-point of BD. That is,

or

**Example 2:**

if , , are three non-zero complex numbers such that where then prove that the points corresponding to , , and are collinear.

**Solution:**

latex \frac{(1-\lambda)z_{1}+\lambda z_{2}}{1-\lambda +\lambda}$.

Hence, divides the line joining and in the ratio . Thus, the given points are collinear.

**Homework:**

- Let , , be three complex numbers and a, b, c be real numbers not all zero, such that and . Show that , , are collinear.
- In triangle PQR, , , and are inscribed in the circle . If be the orthocentre of triangle PQR, then find .

More later,

Nalin Pithwa

### Like this:

Like Loading...

*Related*