- #1

- 3,077

- 4

N

_{[pi]}(a

_{n}+ib

_{n})=C

n=1

such as by representation with vectors in the complex plane, or algebraic simplification? Specifically, I would like to know the value Re(C).

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Loren Booda
- Start date

- #1

- 3,077

- 4

N

n=1

such as by representation with vectors in the complex plane, or algebraic simplification? Specifically, I would like to know the value Re(C).

- #2

- 85

- 0

Any complex number a+ib can be represented as R(& theta). Where R is the magnitude and & theta is the phase. So convert the complex number into R(& theta) form and multiply. The R parts multiply while the angle parts add up.

e.g. R(& theta)* P(& Theta) = R*P(& theta + & Theta)

Got it???

Sridhar

- #3

- 3,077

- 4

Can you or another be more mathematical in regard to the transform involved?

Is it tan

- #4

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

if (a + bi) = r exp(iθ), then it is true that

r = (a^2 + b^2)^(1/2)

and

tan θ = b/a

But you have to make sure that θ is in the correct quadrant. (iow you might have to add π).

- #5

- 3,077

- 4

Is there a simplifying (exact) identity for the arithmetic series

N

[sum]tan

n=1

and for the geometric series

N

n=1

or, more importantly,

Share: