0
$\begingroup$

Possible Duplicate:
Do “imaginary” and “complex” angles exist?

Do Situations ever arise where angles can be complex?

If they are already in use what geometrical or other interpretation do they have?

The fact that De Moivre's theorem works well even when the powers are complex numbers is a good idea but I do not remember dealing with complex angles.

Added : By angle being complex, I mean, just like complex numbers, angles being in the form of $a+ib$, My question explicitly is what would be the meaning of $90i^0$ or $\sin(90i^0)$?

Added I just realized that it is almost exact duplicate of the post suggested below. It can be at best deleated or else closed.

$\endgroup$
1
  • $\begingroup$ What does it mean for an angle to be complex? $\endgroup$
    – davidlowryduda ♦
    Jan 6, 2013 at 10:29

3 Answers 3

Reset to default
2
$\begingroup$

Well yes and no. I am not familiar with a use of complex numbers to describe actual angles, but complex numbers are used to describe phase (which can be thought of as an angle).

A complex phase means that the real part gives the physical phase shift whereas the imaginary part gives the measure of the decay for the signal: $$re^{i\phi},\ \phi=a+bi \rightarrow \ (r e^{-b})e^{ia}$$

$\endgroup$
2
$\begingroup$

Well, we do have the following formulas that give meaning to complex angles: $$ \sin(z) = \frac{1}{2} (e^{iz} - e^{-iz}) \quad \text{and} \quad \cos(z) = \frac{1}{2} (e^{iz} + e^{-iz}). $$ There are applications of complex angles to physics, especially in the fields of quantum mechanics and optics. You may want to refer to this MSE thread.

$\endgroup$
1
$\begingroup$

Your notation $90i^o$ does not make sense. Angles are used just for geometric interpretation of complex numbers as points in complex plane. Notion of complex angle is apsurd at this time in future who know

$\endgroup$

Not the answer you're looking for? Browse other questions tagged .