- #1

nicemaths

- 2

- 0

**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 dont know where to go to find y,

i did tan(y) = π/3 but after than i dont know where to go

thanks for the help !