Express exp(3+Pi*i) in Cartesian Form

[nicemaths]

The problem statement
Express exp(3+π*i) in Cartesian Form.

The attempt at a solution
Equating
e^(3+πi) = e^(x)e^(iy) = e^(x)(cos(y) + isin(y))
then
e^(x)cos(y) = 3
e^(x)sin(y)=π
now
|e^(3+πi)| = e^(x)
so x = sqrt(9+π^2)
then
cos(y) = 3/sqrt(9+π^2)
sin(y) = π/sqrt(9+π^2)

at this point i don't know where to go to find y,
i did tan(y) = π/3 but after than i don't know where to gothanks for the help !

 

[mjc123]

e^(x)cos(y) = 3
e^(x)sin(y)=π

How do you get this? x=3, y=π. What is e³? What is cos π? What is sin π?

 

[nicemaths]

How do you get this? x=3, y=π. What is e³? What is cos π? What is sin π?

oh deary me, i feel silly now that i see the huge error

 

[mjc123]

No need to feel silly, we all make mistakes, just learn from them.