Given z=cosx+isinx, show cosx=1/2(z+1/z)
We first consider 1/z=(cosx+isinx)^(-1). Application of De Moivre's theorem for integer n: (cosx+isinx)^(n)=cosnx+isinnx yields the result 1/z=cosx-isinx. Addition of the two forms z and z^(-1) steers us to the result, albeit with this being double the result.
CS
Answered by Chris S. • Further Mathematics tutor
9660 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸How do you calculate the cross product of two vectors?
The set of midpoints of the parallel chords of an ellipse with gradient, constant 'm', lie on a straight line: find its equation; equation of ellipse: x^2 + 4y^2 = 4
Find all of the roots of unity, Zn, in the case that (Zn)^6=1
Given that f(x)=2sinhx+3coshx, solve the equation f(x)=5 giving your answers exactly.