CameraIcon

SearchIcon

MyQuestionIcon

1

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

Modulus of a Complex Number

The principal...

Question

The principal amplitude of $(2 - i) (1 - 2 i)^{2}$ is in the interval :

A

(0, \frac{π}{2})

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

B

(- \frac{π}{2}, 0)

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

C

(- π, - \frac{π}{2})

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

D

(\frac{π}{2}, π)

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

Open in App

Solution

The correct option is C $(- π, - \frac{π}{2})$
Given $(2 - i) (1 - 2 i)^{2} = - 10 - 5 i$
$∴ (x, y) = (- 10, - 5)$
Since $(- 10, - 5)$ belongs to third quadrant
Hence interval will be $(- π, - \frac{π}{2})$

Suggest Corrections

thumbs-up

1

Similar questions

Which of the following is the principal value branch of $c o s e c^{- 1} x ?$

(a) $(\frac{- π}{2}, \frac{π}{2})$ (b) $[0, π] - {\frac{π}{2}}$ (c) $[\frac{π}{2}, \frac{π}{2}]$ (d) $[\frac{- π}{2}, \frac{π}{2}] - [0]$

Which of the following is the principal value branch of $c o s^{- 1} x ?$

(a) $[- \frac{π}{2}, \frac{π}{2}]$ (b) $(0, π)$ (c) $[0, π]$ (d) $(0, π) - {\frac{π}{2}}$

The amplitude of $\frac{1}{i}$ is equal to

f : (- 1, 1) \to B

, be a function defined by

f (x) = t a n^{- 1} \frac{2 x}{1 - x^{2}}

, then f is both one - one and onto when B is the interval

Q. The intervals for which

tan x > cot x

x \in (0, π) - {\frac{π}{2}}

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Modulus of a Complex Number

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon