Raising Complex Numbers to Powers of Angles - What Happens?

  • Thread starter Thread starter Andrea2
  • Start date Start date
  • Tags Tags
    Angles
Andrea2
Messages
9
Reaction score
0
is there anyone who can tell me what happen when i raise a complex number to the power of an angle in rad? for example, what is the result of (i)^1rad?
 
Mathematics news on Phys.org
is there anyone who can tell me what happen when i raise a complex number to the power of an angle in rad? for example, what is the result of (i)^1rad?
Since you ask about the power of a COMPLEX number, so I suppose that you already know what happen when you raise a REAL number to the power of an angle in rad. For example, what is the result of 2^1rad ?
 
i don't know exactly what happen if i raise a real number to the power of an angle, i tried to answer also to this question, but five minutes ago i think I've found the answer to my first question, and i think that this problem is more difficult with real numbers than with complex! My solution is that (i)^a = e^(a x log(i)) with a=angle in rad. log(i) = i x p/2 (p=3.1416...), so (i)^a = e^(i x ap), that is a complex number...
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

I Raising to the power of 0 or 1
Replies
17
Views
2K
Insights Fixing Things Which Can Go Wrong With Complex Numbers
Replies
7
Views
758
I Formal definition of multiplication for real and complex numbers
Replies
2
Views
2K
Insights Views On Complex Numbers
3
Replies
108
Views
10K
A How Does U(1) Double-Cover SO(2) for a Specified Angle?
Replies
2
Views
2K
I Newton-Raphson Method With Complex Numbers
Replies
7
Views
2K
I Constant raised to complex numbers
Replies
14
Views
2K
I Properties of the legs of a right triangle
Replies
3
Views
1K
I Principal difference between complex numbers and 2D vectors revisited
Replies
24
Views
3K
I Division of a complex number by zero
Replies
7
Views
4K

Hot Threads

Recent Insights

Back
Top