Complex number arithmetic.
evaluate:
e^(1 + i*pi/4)
final result in cartesian form but im confused on where to start.

I know its equivalent to e*e^(i*pi/4)
I dont see how that would help me tho.

Question

Complex number arithmetic.
evaluate:
e^(1 + i*pi/4) 
final result in cartesian form but im confused on where to start.

I know its equivalent to e*e^(i*pi/4)
I dont see how that would help me tho.

aum · Answer

$$\large e^{1 + i\pi/4} = e * e^{i\pi / 4} = e * (\cos\pi/4 + i\sin\pi/4) = ?$$

anonymous · Answer

= e*(cos(pi/4)) + e*i*sin(pi/4).
then x = ecos(pi/4) = (e*sqrt(2))/2
        y = esin(pi/4)  = same as above
thus, z= (e*sqrt(2))/2 + i(e*sqrt(2))/2 ??

aum · Answer

yes.

anonymous · Answer

great thanks I forgot about that essetial identity...

aum · Answer

You are welcome.