help@askiitians.com

1800-150-456-789

Algebra> If the complex number z1,z2 ,z3 represent...

question mark

If the complex number z1,z2 ,z3 represent the vertices of an equilateral triangle such that |z1|=|z2|=|z3|, then find z1+z2+z3

Harshit , 8 Years ago

Grade 11

2 Answers

mycroft holmes

Last Activity: 8 Years ago

Here circumcentre is the origin O. Let the vertices be A,B,C. We have angles AOB = BOC = COA = 120^o 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 $z_1+z_2+z_3 = z_1(1+\omega + \omega^2 ) = 0$

mycroft holmes

Last Activity: 8 Years ago

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

Provide a better Answer & Earn Cool Goodies

Enter text here...

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

What is a binomial expression?

algebra

1 Answer Available

Last Activity: 1 Year ago

Can we divide two vectors? If this is possible then how?

algebra

1 Answer Available

Last Activity: 1 Year ago

How do you write “the product of 18 and q” as an algebraic expression?

algebra

1 Answer Available

Last Activity: 1 Year ago

दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे

algebra

0 Answer Available

Last Activity: 2 Years ago

Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?

algebra

1 Answer Available

Last Activity: 2 Years ago

View all Questions