How would you prove that z - 1/z = 2*j*sin(theta) ?

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- Jun 8th 2013, 10:38 AMyugimutoshungProving for complex numbers
How would you prove that z - 1/z = 2*j*sin(theta) ?

- Jun 8th 2013, 10:56 AMPlatoRe: Proving for complex numbers
- Jun 8th 2013, 11:04 AMyugimutoshungRe: Proving for complex numbers
I think "z" refers to r*cis(theta)

- Jun 8th 2013, 11:32 AMPlatoRe: Proving for complex numbers
- Jun 8th 2013, 12:03 PMMINOANMANRe: Proving for complex numbers
- Jun 8th 2013, 12:23 PMPlatoRe: Proving for complex numbers
I don't understand if you meant comment for me or for the OP.

As I said it is true if $\displaystyle |z|=1$ it is true. Here is the standard proof.

Recall that if $\displaystyle z=\text{c}i\text{s}(\theta)$ then $\displaystyle \frac{1}{z}=\text{c}i\text{s}(-\theta)$.

Now it is just a exercise to finish.