Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
        If the complex number z1,z2 ,z3 represent the vertices of an equilateral triangle such that |z1|=|z2|=|z3|, then find z1+z2+z3
2 years ago

mycroft holmes
272 Points
							Here circumcentre is the origin O. Let the vertices be A,B,C. We have angles AOB = BOC = COA = 120o and OA = OB = OC since its given that |z1| =  |z2| =  |z3|So we have $z_2 = z_1 \omega, z_3 = z_1 \omega^2$ where $\omega = e^{\frac{2\pi i}{3} }$ is the primitive cube root of infinity. So$z_1+z_2+z_3 = z_1(1+\omega + \omega^2 ) = 0$

2 years ago
mycroft holmes
272 Points
							Shorter way to go about it is: Invoke the result that if the circumcenter is at the origin then the complex number corresponding to the orthocenter is z1+z2+z3. Since the triangle is equilateral, orthocenter and circumcenter coincide. So we have z1+z2+z3 = 0

2 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »

### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution

### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions