How to Express a Complex Number in the Form of I-Tan(kA)?

AI Thread Summary
To express the complex number z = CosA + iSinA in the form I-Tan(kA), the discussion revolves around simplifying the expression 2/(1+z). The challenge lies in manipulating the expression using trigonometric identities and de Moivre's theorem. One suggested method involves multiplying by the conjugate (1-z) to simplify the denominator. The goal is to rewrite the result in the desired format, which may require further simplification. Ultimately, the solution hinges on correctly applying these mathematical principles.
floped perfect
Messages
17
Reaction score
0
Someone solve this please!

If z= CosA+iSinA, express 2/1+z in the form I-Tan(kA).
 
Mathematics news on Phys.org
Well,what is that number (2/(1+z)) equal to?

And what do you mean by "I-Tan(kA)"...?

Daniel.
 
where k is a constant and A is the angle from above, it says to express the answer in that form- z is a complex number in polar form.
I tried multiplying the 2/(1+z) by the conjugate (1-z) on the top and bottom but I can't get it into the form 1-Tan(kA).
I think this involves trignometric identities and de Moivre's theorem.
 
you write z as (cosA + i SinA) and multilply the denominator by (1+ CosA --iSinA)...Simplify it...
Answer will come
 

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 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

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 Is it valid to express a complex number as a vector?
Replies
8
Views
2K
I Formal definition of multiplication for real and complex numbers
Replies
2
Views
2K
I Newton-Raphson Method With Complex Numbers
Replies
7
Views
3K
MHB Max Value of |bc| for Complex Numbers in Inequality
Replies
2
Views
1K
MHB Finding Real Part of $z$ for Complex Numbers
Replies
1
Views
1K
B How can complex numbers be elevated to complex powers?
Replies
12
Views
3K
I How can you represent a point by "z = x + iy" as shown here?
Replies
10
Views
2K
B Principal square root of a complex number, why is it unique?
Replies
13
Views
5K
I Relation between a circle and line in complex plane
Replies
16
Views
2K
MHB 1.4.1 complex number by condition
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top