You are Here: Home >< Maths

# Hard complex numbers question (De Moivre's) watch

1. A) Express e^ix/2 - e^-ix/2 in terms of sin x/2

Fairly simple

B) Hence, or otherwise, show that 1/(e^(ix) -1) = -1/2 - i/2 (cot (x/2)).

Have no clue, obviously you can simplify the cot to give i/2tan(x/2) but other than that not sure really, especially with the hence.

Help appreciated

NOTE: I know I post a lot but it's only because 1. I love maths and 2. I do a lot of questions
2. (Original post by psycholeo)
A) Express e^ix/2 - e^-ix/2 in terms of sin x/2

Fairly simple

B) Hence, or otherwise, show that 1/(e^(ix) -1) = -1/2 - i/2 (cot (x/2)).

Have no clue, obviously you can simplify the cot to give i/2tan(x/2) but other than that not sure really, especially with the hence.

Help appreciated

NOTE: I know I post a lot but it's only because 1. I love maths and 2. I do a lot of questions

How can you you use part A? Clearly it relates to the denominator. So, what could you multiply the top and bottom of the fraction by to get the denominator in the form of part A?...
3. rearrange your answer to part A to get an expression for e^ix in terms sin(x/2), substitute this into B and replace i/2tan(x/2) by i/2sin(x/2)/cos(x/2) and simplify.
4. (Original post by ghostwalker)

How can you you use part A? Clearly it relates to the denominator. So, what could you multiply the top and bottom of the fraction by to get the denominator in the form of part A?...
Multiply top and bottom by e^-ix/2?
5. (Original post by psycholeo)
Multiply top and bottom by e^-ix/2?
Yep, and then you can sub in from part A, etc. (I assumed you'd go ahead and do it).

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 5, 2018
Today on TSR

### The TSR A-level options discussion thread

Choosing A-levels is hard... we're here to help

### University open days

• Heriot-Watt University
School of Textiles and Design Undergraduate
Fri, 16 Nov '18
• University of Roehampton
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE