You visited us 1 times! Enjoying our articles? Unlock Full Access!

Section Formula Using Complex Numbers

Let A, B, C...

Question

Let $A, B, C$ represent the complex number $z_{1}, z_{2}, z_{3}$ respectively on the complex plane. If the circumcentre of the triangle $A B C$ lies at the origin, then the orthocentre is represented by the complex number.

z_{1} + z_{2} - z_{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

z_{2} + z_{3} - z_{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

z_{3} + z_{1} - z_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

z_{1} + z_{2} + z_{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $z_{1} + z_{2} + z_{3}$
Centre of the circle is ato origin $= 0$
Centroid $= \frac{z_{1} + z_{2} + z_{3}}{3}$
Refer image
From orthocentre, $O C = 3 P C = \frac{3 (z_{1} + z_{2} + z_{3})}{3}$
$= z_{1} + z_{2} + z_{3}$
The orthocentre complex no. is $z_{1} + z_{2} + z_{3}$

Suggest Corrections

Similar questions

z_{1}, z_{2}, z_{3}

| z_{1} | = | z_{2} | = | z_{3} |,

z_{1} + z_{2} + z_{3} =

z_{1}, z_{2}, z_{3}

\frac{1}{z_{1} - z_{2}} + \frac{1}{z_{2} - z_{3}} + \frac{1}{z_{3} - z_{1}} = 0

z_{1}, z_{2}, z_{3}

| z_{1} | = | z_{2} | = | z_{3} |

z_{1} + z_{2} + z_{3} = 0

z_{1}, z_{2}, z_{3}

z_{2} \neq 1, a = | z_{1} |, b = | z_{2} |

c = | z_{3} |

∣ ∣ ∣ ∣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ∣ ∣ ∣ ∣ = 0

z_{1}, z_{2}, z_{3}

| z_{1} | = | z_{2} | = | z_{3} | = ∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ ∣ = 1

| z_{1} + z_{2} + z_{3} |

Join BYJU'S Learning Program