NPTEL IIT Guwahati

Find the values of which make the function $f(z) = \exp(z)$ (a) purely real and (b) purely imaginary.
Prove that where $\Im(z)$ denotes the imaginary part of . Deduce that tends to $\infty$ as .
(Note that $\sin(z)$ is an unbounded complex-valued function of a complex variable whereas $\sin(x)$ for $x \in \QTR{Bbb}{R}$ is a bounded real-valued function of a real variable.).
Find all solutions of $\exp(z-1) = 1$

Describe the image of the following sets in the -plane under the mapping $w = \sin(z)$ .
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)


Elementary Analytic Functions and their Mapping Properties		Print this page

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Find the values of which make the function $f(z) = \exp(z)$ (a) purely real and (b) purely imaginary. Prove that where $\Im(z)$ denotes the imaginary part of . Deduce that tends to $\infty$ as . (Note that $\sin(z)$ is an unbounded complex-valued function of a complex variable whereas $\sin(x)$ for $x \in \QTR{Bbb}{R}$ is a bounded real-valued function of a real variable.). Find all solutions of $\exp(z-1) = 1$ Describe the image of the following sets in the -plane under the mapping $w = \sin(z)$ . (i) (ii) (iii) (iv) (v) (vi) (vii)

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