Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The function $f : \mathbb{C} \to \mathbb{C}$ defined by $f(z) = z - \bar{z}$ is analytic at every point in $\mathbb{C}$ Reason R : $f$ does not satisfy the Cauchy - Riemann equations at any point.
In the light of the above statements, choose the correct answer from the options given below

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

Any function containing $\bar{z}$ explicitly (such as $z - \bar{z} = 2i \text{Im}(z)$) fails C-R equations almost everywhere and is non-analytic!

Answer 1

The Correct Option is D