Find the set of values, which are taken by tan⁡z I was trying to write...

treetopssan

treetopssan

Answered

2022-01-27

Find the set of values, which are taken by tanz
I was trying to write tangents as follows:
tan(z)=ieizeizeiz+eiz
and then
z=a+bi
, which led me to
tanz=icosa(ebeb)+isina(eb+eb)cosa(eb+eb)+isina(ebeb)

Answer & Explanation

izumrledk

izumrledk

Expert

2022-01-28Added 15 answers

It is much easier to deal with this problem using the fact that
1+tan2(z)=1cos2(z)
So, which numbers can be written as 1cos2(z)? Answer: all, except 0. It follows from this (and from the fact that tan is an odd function), that the range of tan  is  C{±i}
Jude Carpenter

Jude Carpenter

Expert

2022-01-29Added 9 answers

HINT
We have that by the standard trick
tan(z)=ieizeizeiz+eizeiz+eizeiz+eiz=
then use the well know identities for cos,sin,cosh  and  sinh

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?