Home
Class 12
MATHS
Let z1 and z2q, be two complex numbers ...

Let `z_1 and z_2`q, be two complex numbers with `alpha and beta` as their principal arguments such that `alpha+beta` then principal `arg(z_1z_2)` is given by:

A

`alpha+beta+pi`

B

`alpha+beta-pi`

C

`alpha+beta-2pi`

D

`alpha+beta`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `arg(z_(1)z_(2))=arg(z_(1))+arg(z_(2))+2mpi`, `m in I`
`:.` Principal argument `=alpha+beta-2pi`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Multiple Correct Answer|11 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Matching Column|1 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|16 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|87 Videos

Similar Questions

Explore conceptually related problems

Let z_(1)" and "z_(2) be two complex numbers such that z_(1)z_(2)" and "z_(1)+z_(2) are real then

Let z be any non zero complex number then arg z + arg barz =

The principal value of arg(z) lies in the interval :

It z_(1) and z_(2) are two complex numbers, such that |z_(1)| = |z_(2)| , then is it necessary that z_(1) = z_(2) ?

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( barz )_2dot

If z_1 and z_2 are two complex number such that |z_1|<1<|z_2| then prove that |(1-z_1 bar z_2)/(z_1-z_2)|<1

Let A(z_1) and (z_2) represent two complex numbers on the complex plane. Suppose the complex slope of the line joining A and B is defined as (z_1-z_2)/(bar z_1-bar z_2) .If the line l_1 , with complex slope omega_1, and l_2 , with complex slope omeg_2 , on the complex plane are perpendicular then prove that omega_1+omega_2=0 .

If alpha" and "beta are complex numbers such that |beta|=1, " then "|(beta - alpha)/(1-bar(alpha)beta)|=