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

astarmathsandphysics:
Gimme am hour to get to c pc

astarmathsandphysics:
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))

Syeda Zuriat Zahra:
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.

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

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