IIT JEE , AIEEE Forum - Mathematics , Algebra

sumeet

if

z=ilog(2-

3)

find cosz?

i' ve tried as follows:

please say whether my process is correct

firstly i' ve considered the base to be 'e';

hence,

z=log_e(2-

3)ⁱ ; e^z/i =2-

3 ; e^-iz=2-

3 ; cosz-isinz=2-

3;

hence cosz=2-

3.

^[

titun

I think the question is wrong.

This is because z is purely immaginary and cosz is not defined. (since trigonometric function of an immaginary quantity is not defined)

The correct question should be:

Find out cos(mod.z) ?

Ans: In this case, mod.z = -log(2-

3) [negative sign is because mod.z is always a positive quantity]

So, cos(mod.z) = cos(log(2-

3))

A far as sumeet's solution is concerned, log_e(2-

3)ⁱ

^{is not defined. So, your solution is incorrect.}

edison

Dear sumeet i think your approach is fair enough and ok.

sanjeev_mishra

e^{iz _=2-}

3 means cos

+isin

=2-

3

then e^{-iz_{=cos-sin=-2-3}}

_{^{then adding we get cos=-23 (ans)}}

sanjeev_mishra

e^{iz _=2-}

3 means cos

+isin

=2-

3

then e^{-iz_{=cos-sin=-2-3}}

_{^{then adding we get cos=-3 (ans)}}

mohit1

Z = ilog(2-root3) is a purely imaginary number.how can cosz be defined?

mohit1

mohit1

Someone tell me please