IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => University => Topic started by: Syeda Zuriat Zahra on November 21, 2009, 09:47:00 am

Title: Complex analysis
Post by: Syeda Zuriat Zahra on November 21, 2009, 09:47:00 am

Can anyone solve this question
Find the value of z for which sinz=2i and cosz=2.

Title: Re: Complex analysis
Post by: astarmathsandphysics on November 21, 2009, 09:50:36 am

Gimme am hour to get to c pc

Title: Re: Complex analysis
Post by: astarmathsandphysics on November 21, 2009, 11:20:32 am

cosz=2
cos(x+iy)=cosxcoshy-isinxsinhy=2 so  cosxcoshy=2 (1) and -sinxsinhy=0 and x=n pi  but from (1) cosh is positive so cos is positve and x=2npi and from (2) y=cosh^-1(-2)

sinz=2i so sinxcoshy+icosxsinhy=2i so sinxcoshy=0 cosxsinhy=2 (2)
from 1st equationx=npi and from second sinhy=2/cos(n pi) so y =sinh^-1(2/cos(n pi))

Title: Re: Complex analysis
Post by: Syeda Zuriat Zahra on November 22, 2009, 06:53:02 am

No you are doing it all wrong. i know it a little bit but i don't now how to solve it till the end. I'll give you a hint
cosz=2
cos(x+iy)=2
cosxcoshy-isinxsinhy=2+0i
cosxcoshy=2     -sinxsinhy=0     now i cannot solve further.

Title: Re: Complex analysis
Post by: astarmathsandphysics on November 22, 2009, 08:10:15 am

I am so stupid. How did i make that mistake. Will do it when i get up.

Title: Re: Complex analysis
Post by: Syeda Zuriat Zahra on November 23, 2009, 04:54:43 pm

How did you get the value of x? mostly do it by putting sinhy not=0 and sinx=0, x=sin^-10
x=npi but this is wrong. how can we put sinhy not=0 because sinh0=0.

Title: Re: Complex analysis
Post by: SGVaibhav on November 23, 2009, 05:52:36 pm

this is weird analysis.

sounds like a different language.

i dont know anything about this

but i just used this on a search engine called Wolfram alpha
lol it solved the question but the input is wrong :(
try it out urself :D

http://www.wolframalpha.com/input/?i=sinz%3D2i+cosz%3D2

Title: Re: Complex analysis
Post by: astarmathsandphysics on November 23, 2009, 10:10:57 pm

sin npi=0 Try it

Title: Re: Complex analysis
Post by: SGVaibhav on November 26, 2009, 09:38:02 am

is it something taught to students in maths while obtaining a bachelors degree?
or is it taught to students in maths when they r obtaining a masters degree?

Title: Re: Complex analysis
Post by: astarmathsandphysics on November 26, 2009, 10:01:19 am

Actually that is part of further maths at a level probably.

Title: Re: Complex analysis
Post by: Syeda Zuriat Zahra on November 27, 2009, 04:13:44 am

nope. its at the master level