CameraIcon

SearchIcon

MyQuestionIcon

47

You visited us 47 times! Enjoying our articles? Unlock Full Access!

Local Maxima

If z 1, z 2, ...

Question

If $z_{1}, z_{2}, z_{3}$ be three non-zero complex number, such that $z_{2} \neq z_{1}, a = | z_{1} |, b = | z_{2} | a n d c = | z_{3} |$ suppose that
$∣ ∣ ∣ ∣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ∣ ∣ ∣ ∣ = 0, t h e n a r g (\frac{z_{3}}{z_{2}})$ is equal to

A

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

B

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

C

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

D

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

Open in App

Solution

The correct option is C
First deduce that a = b = c, then it will be equal to $a r g {(\frac{z_{3} - z_{1}}{z_{2} - z_{1}})}^{2}$ .

Suggest Corrections

thumbs-up

0

Similar questions

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

be three non-zero complex number, such that

z_{2} \neq z_{1}, a = | z_{1} |, b = | z_{2} | a n d c = | z_{3} |

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

(\frac{z_{3}}{z_{2}})

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

be complex number such that

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

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

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

be the complex numbers such that

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

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

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

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

are complex number 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

Extrema

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon