[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) e^{i pi} I have the answer -1.
b) e^{i 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.

Thank you in advance.

[f1mad]

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)

[mld]

(Original post by f1mad)
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

[james22]

(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) e^{i pi} I have the answer -1.
b) e^{i 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.

Thank you in advance.

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.

[mld]

(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.

[james22]

(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.