Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The map $f : \mathbb{C} \to \mathbb{C}$ defined by $f(z) = \sin z$ is bounded. Reason R : The function $f(z) = \sin z$ is an entire map.
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:

Do not confuse real trigonometric functions with complex ones! On $\mathbb{R}$, $|\sin x| \leq 1$. On $\mathbb{C}$, $|\sin z|$ grows towards $\infty$ along the imaginary axis!

Answer 1

The Correct Option is D