You are Here: Home >< Maths

# Complex modulus proof watch

1. The question and what I've done so far:

http://i1352.photobucket.com/albums/...psb591132c.jpg

The blue bit is from the mark scheme - but I don't understand how they have come to this
And the red bits are 'rules' we can use for modulus

I've written out the complex and the complex conjugate but not sure what to do!
2. Well first, sub in z= r ( cosθ + i sinθ ) into the modulus. Then simply take the modulus of the thing which is root of real part squared plus imaginary part squared (the root goes away because the modulus is squared in the question) . So your real part is rcosθ + 1 and imaginary part is -rsinθ. Then just expand the brackets.
This is the same as finding the modulus of eg : 3 + 2i. you would do
√ 3^2 + 2^2. you are doing the same thing here
3. use the last rule to begin with, i.e

(since the conjugate of is )

expand that top line,
replace the ( z z bar) with mod z squared,
then sub in the polar forms and you should get the result

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: April 8, 2013
Today on TSR

### Three reasons you may feel demotivated right now

...and how to stay positive

### Can I get A*s if I start revising now?

Discussions on TSR

• Latest
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
Discussions on TSR

• Latest

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