MyQuestionIcon

1

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

Complex Numbers

If z1=1+2i,...

Question

If $z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i$ , then $z_{1}, z_{2}$ and $z_{3}$ are collinear.

A

True

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

B

False

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

Open in App

Solution

The correct option is A True
Line formula from $z_{3}$ and $z_{1}$
$(y - y_{1}) = \frac{y_{3} - y_{1}}{x_{3} - x_{1}}$ $\times (x - x_{1})$
$⟹ (y - 2) = \frac{(4 - 2) (x - 1)}{3 - 1}$
$⟹ y - 2 = x - 1 ⟹ y = x + 1$
$z_{2} = (2, 3)$
$y = x + 1$ satisfies $z_{2}$ .
Hence $z_{1}, z_{2}$ and $z_{3}$ are collinear.

Suggest Corrections

thumbs-up

0

Similar questions

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i,

z_{1}, z_{2}

z_{3}

represent the vertices of

State True and False

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i,

z_{1}, z_{2}

z_{3}

Type 1 for true and 0 for false

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i, p r o v e t h a t t h e n z_{1}, z_{2} a n d z_{3}

z_{1}, z_{2}

z_{3}

are complex numbers such that

| 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} |

z_{1}, z_{2}

z_{3}

are complex numbers such that

| 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} |

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Complex Numbers

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon