MyQuestionIcon

1

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

Argument of a Complex Number

If arg z1=π...

Question

If $a r g z_{1} = \frac{π}{2}$ , $a r g {¯ ¯ ¯ z}_{2} = \frac{π}{4}$ , then $a r g (\frac{z_{1}}{z_{2}}) =$

A

\frac{π}{4}

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

B

- \frac{π}{2}

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

C

- \frac{π}{4}

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

D

\frac{3 π}{4}

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

Open in App

Solution

The correct option is D $\frac{3 π}{4}$
$a r g (z_{1}) = \frac{π}{2}$
and $a r g (_{2}) = \frac{π}{4}$
Therefore, $a r g (z_{2}) = \frac{- π}{4}$ .
Now
$a r g (\frac{z_{1}}{z_{2}})$

$= a r g (z_{1}) - a r g (z_{2})$
$= \frac{π}{2} - (- \frac{π}{4})$

$= \frac{2 π}{4} + \frac{π}{4}$

$= \frac{3 π}{4}$ .

Suggest Corrections

thumbs-up

0

Similar questions

| z_{1} - z_{2} | = | z_{1} | + | z_{2} |

, then prove that

a r g (z_{1}) - a r g (z_{2}) = π

z_{1}, z_{2}

are complex numbers then the correct match List- I to List II is:

List - I	List - II
A) arg z_1z_2	1) $a r g z_{1} - a r g z_{2}$
B) $a r g z_{1}_{2}$	2) $a r g z_{1} - a r g z_{2} = \frac{π}{2}$
C) $\| z_{1} + z_{2} \| = \| z_{1} - z_{2} \|$	3) $a r g z_{1} = a r g z_{2}$
D) $\| z_{1} + z_{2} \|^{2}$	4) $a r g z_{1} + a r g z_{2}$
E) $\| z_{1} + z_{2} \| = \| z_{1} \| + \| z_{2} \|$	5) $r_{1}^{2} + r_{2}^{2} + 2 r_{1} r_{2} c o s (θ_{1} - θ_{2})$

z_{1}

z_{2}

are two complex numbers such that

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

a r g z_{1} + a r g z_{2} = π

z_{1}

z_{2}

z_{1}

z_{2}

are two non-zero complex numbers such that

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

a r g z_{1} + a r g z_{2} = π

z_{2}

Q. The intervals for which

tan x > cot x

x \in (0, π) - {\frac{π}{2}}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Geometric Representation and Trigonometric Form

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Argument of a Complex Number

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon