You are Here: Home >< Maths

# Complex Numbers With Logarithms! Watch

1. I'm not really sure how to go about solving these, by 'principal values' I assume the values you get from finding the argument right?

For Question 14 would I use laws of logs to solve?
2. (Original post by As_Dust_Dances_)

I'm not really sure how to go about solving these, by 'principal values' I assume the values you get from finding the argument right?

For Question 14 would I use laws of logs to solve?
Basically, there are many values the logarithm of a complex number could take - you could say log(1)=0, because e^0=1, but equally e^(2pi i)=1, so you could say log(1)=2pi i.

To get around this, we say that the principal value of the logarithm of a complex number is the one whose imaginary part is greater than -pi, and less than or equal to pi.
3. (Original post by Mark13)
Basically, there are many values the logarithm of a complex number could take - you could say log(1)=0, because e^0=1, but equally e^(2pi i)=1, so you could say log(1)=2pi i.

To get around this, we say that the principal value of the logarithm of a complex number is the one whose imaginary part is greater than -pi, and less than or equal to pi.
Thanks for your help, took me a while to understand it but essentially you can write it in the form (which I think is what you were saying)

log(z) = ln|z| + i arg(z) which is how I solved it.

Thanks again!

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 2, 2013
Today on TSR

### Last-minute PS help

100s of personal statements examples here

### Loneliness at uni

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• 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
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• 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

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.