help adding complex numbers!

[yersinia29]

e^(i*2pi/3) + e^(i*4pi/3)

Now I think that the result of this should be:

= e^(i*6pi/3) = e^(i*2pi) = 1 (one full rotation around the unit circle.

However, when I add this in my calculator, it says teh answer is -1, not 1.

Whats the deal?

[Badly Shaved Monkey]

Originally posted by yersinia29
e^(i*2pi/3) + e^(i*4pi/3)

Now I think that the result of this should be:

= e^(i*6pi/3) = e^(i*2pi) = 1 (one full rotation around the unit circle.

However, when I add this in my calculator, it says teh answer is -1, not 1.

Whats the deal?

Your calculator has an i button?

[Diamond]

Originally posted by yersinia29
e^(i*2pi/3) + e^(i*4pi/3)

Now I think that the result of this should be:

= e^(i*6pi/3) = e^(i*2pi) = 1 (one full rotation around the unit circle.

However, when I add this in my calculator, it says teh answer is -1, not 1.

Whats the deal?

Excuse me, but the only time you should add the powers like that is when the two parts are multiplied not added

[Drooper]

I think you need to factorise and then apply Euler. I shall say no more, because nobody ever helped me with my maths homework. :p

[Pragmatist]

Originally posted by yersinia29
e^(i*2pi/3) + e^(i*4pi/3)

Now I think that the result of this should be:

= e^(i*6pi/3) = e^(i*2pi) = 1 (one full rotation around the unit circle.

However, when I add this in my calculator, it says teh answer is -1, not 1.

Whats the deal?

Yep, the answer is -1.

Just use Euler's formula and sum the parts.

[CurtC]

Diamond is right - if the exponents are added, that's equivalent to multiplying the numbers. You need to change them to rectangular coordinates, then add the real and imaginary parts.

[jj]

Originally posted by yersinia29
e^(i*2pi/3) + e^(i*4pi/3)

Now I think that the result of this should be:

= e^(i*6pi/3) = e^(i*2pi) = 1 (one full rotation around the unit circle.

However, when I add this in my calculator, it says teh answer is -1, not 1.

Whats the deal?

Well, first, it's addition, not multiplication, so you don't add the exponents.

Now, let's look at the angles. The two numbers are complex conjugates, they are zero (or pi) +- a fixed amount, so the imaginary parts are going to cancel


Now you just need to figure out the magnitude. Easiest way is to just figure out the real parts via Euler's formula and add them together, since you already know the imaginary parts add to zero, since they are conjugate angles.

[Jorghnassen]

exp(i*theta)=cos(theta)+i*sin(theta)

cos(2pi/3)=-1/2
sin(2pi/3)=sqrt(3)/2

cos(4pi/3)=-1/2
sin(4pi/3)=-sqrt(3)/2

The rest is trivial.