The function w-u-iv-12logx2-y2-i tan-1 yx is not analytic at the point

Given function is w=u+iv=12log(x^2+y^2)+i tan^ 1 ( yx ) This is log z We have w=log z, nbsp;which is obviously not defined at z=0≈ (0,0) So, w=log z is not a ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Graphical Interpretation of Continuity

The function ...

Question

The function $w = u + i v = \frac{1}{2} l o g (x^{2} + y^{2}) + i t a n^{- 1} (\frac{y}{x})$ is not analytic at the point

(0,0)

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

(0,1)

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

(1,0)

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

(2,

α

)

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

Open in App

Solution

The correct option is A (0,0)
Given function is
$w = u + i v = \frac{1}{2} l o g (x^{2} + y^{2}) + i t a n^{- 1} (\frac{y}{x})$
This is $l o g z$
We have $w = l o g z$ , which is obviously not defined at $z = 0 \approx (0, 0)$
So, $w = l o g z$ is not analytic at $(0, 0)$

Suggest Corrections

Similar questions

Q. An analytic function of a complex variabel

z = x + i y

is expressed as

f (x) = u (x, y) + i v (x, y)

where

i = \sqrt{- 1}

. If

u = x y,

the expression for

v

should be

Q. The most general complex analytical function

f (z) = u (x, y) + i v (x, y) f o r u = x^{2} - y^{2}

Q. For an analytic function,

f (x + i y) = u (x, y) + i v (x, y), u

is given by

u = 3 x^{2} - 3 y^{2}

. Th expression for

v

, considering

K

to be a constant is

Q. An analytic function of a complex variable

z = x + i y

is expressed as

f (z) = u (z, y) + i v (x, y),

where

i = \sqrt{- 1}

. if

u (x, y) = 2 x y,

then

v (z, y)

must be

Q. An analytic function

f (z)

of complex variable

z = x + i y

may be written as

f (z) = u (x, y) + i v (x, y)

. Then

u (x, y)

and

v (x, y)

must satisfy.

Join BYJU'S Learning Program

The function w=u+iv=12log(x2+y2)+itan−1(yx) is not analytic at the point

The correct option is A (0,0)Given function is w=u+iv=12log(x2+y2)+itan−1(yx) This is logz We have w=logz, which is obviously not defined at z=0≈(0,0) So, w=logz is not analytic at (0,0)

The function $w = u + i v = \frac{1}{2} l o g (x^{2} + y^{2}) + i t a n^{- 1} (\frac{y}{x})$ is not analytic at the point

The correct option is A (0,0)
Given function is
$w = u + i v = \frac{1}{2} l o g (x^{2} + y^{2}) + i t a n^{- 1} (\frac{y}{x})$
This is $l o g z$
We have $w = l o g z$ , which is obviously not defined at $z = 0 \approx (0, 0)$
So, $w = l o g z$ is not analytic at $(0, 0)$