complex numbers question (1 Viewer)

[lsdpoon1337]

1. if z= cos a + isina

express :
i) 2z/ 1 + z^2
ii) 1- z^2/ 1 + z^2 in x + yi form

where a and y are real functions of a

thanks

 

[shaon0]

1. if z= cos a + isina

express :
i) 2z/ 1 + z^2
ii) 1- z^2/ 1 + z^2 in x + yi form

where a and y are real functions of a

thanks

i) (2cos a + 2isin a)/(cos^2 a -sin^2 a)
= 2cos(a)+2isin(a)/cos(2a)
Go from there

ii) [1-(cos^2 a -sin^2 a)]/[1+(cos^2 a -sin^2 a)]
= 1-cos(2a)/1+cos(2a)
Go from there