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

8138 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

I don't know what I am doing when I solve differential equations using the integrating factor and why does this give us the solutions it does?


How can we solve a limit having an indetermination of the type 0/0 or infinity divided by infinity?


Prove by induction that the sum of the first n integers can be written as (1/2)(n)(n+1).


How to multiply and divide by complex numbers


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences