You are Here: Home

# Euler's formula Tweet

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
Enter our travel-writing competition for the chance to win a Nikon 1 J3 camera 20-05-2013
IMPORTANT: You must wait until midnight (morning exams)/4.30AM (afternoon exams) to discuss Edexcel exams and until 1pm/6pm the following day for STEP and IB exams. Please read before posting, including for rules for practical and oral exams. 28-04-2013
1. Euler's formula
Hi,

I'm doing a post graduate maths course for people who don't have a degree in maths and I'm hoping for some help from some Further Maths people...

The question says, "Use Euler's formula to find,
a) ei pi I have the answer -1.
b) ei pi/3 I have the answer (1 + root 3)/2
and
c) e-i pi/6 I have the answer -(1 + root 3)/2

Now my question to you is how wrong have I got the answers!!!! I really struggle with imaginary number work.

2. Re: Euler's formula
e^itheta= cos(theta)+isin(theta)

Replace theta with pi

-> e^ipi = cos(pi)+isin(pi)

Do the same for the rest.

It is helpful to note: cos(-x)= cos(x). sin(-x)= -sin(x)
3. Re: Euler's formula
e^itheta= cos(theta)+isin(theta)

Replace theta with pi

-> e^ipi = cos(pi)+isin(pi)

Do the same for the rest.

It is helpful to note: cos(-x)= cos(x). sin(-x)= -sin(x)
thank you
4. Re: Euler's formula
(Original post by mld)
Hi,

I'm doing a post graduate maths course for people who don't have a degree in maths and I'm hoping for some help from some Further Maths people...

The question says, "Use Euler's formula to find,
a) ei pi I have the answer -1.
b) ei pi/3 I have the answer (1 + root 3)/2
and
c) e-i pi/6 I have the answer -(1 + root 3)/2

Now my question to you is how wrong have I got the answers!!!! I really struggle with imaginary number work.

Only the first one is right, remember you cannot combine the real and imaginary parts. I'll tell you how to do b), e^(i pi/3)=cos(pi/3)+isin(pi/3)=1/2 + i*root(3)/2. Note that this is in its simplest form and cannot be combined to give (1+root(3)/2 as real and imaginary's cannot be combined.
5. Re: Euler's formula
(Original post by james22)
Only the first one is right, remember you cannot combine the real and imaginary parts. I'll tell you how to do b), e^(i pi/3)=cos(pi/3)+isin(pi/3)=1/2 + i*root(3)/2. Note that this is in its simplest form and cannot be combined to give (1+root(3)/2 as real and imaginary's cannot be combined.
I knew that!!! If there's anything about imaginary numbers that I knew, I did know that. But I forgot.
6. Re: Euler's formula
(Original post by mld)
I knew that!!! If there's anything about imaginary numbers that I knew, I did know that. But I forgot.
But this was the only thing you did wrong, other than that it was all done perfectly.