You are Here: Home >< Maths

# Roots of complex numbers

Announcements Posted on
Why bother with a post grad? Are they even worth it? Have your say! 26-10-2016
1. The question is find the 5th root of 1+2i. I have found r to be sqrt(5) but finding theta is causing me trouble because I'm getting a decimal and I'm not sure how to carry on with a decimal
2. 1+2i can be written as √5*ei*arctan2

so if a 5th root of 1 + 2i is w ....

w5 = √5*ei*arctan2

...
3. (Original post by Lunu)
The question is find the 5th root of 1+2i. I have found r to be sqrt(5) but finding theta is causing me trouble because I'm getting a decimal and I'm not sure how to carry on with a decimal
or you just leave it as a decimal and continue normally?

i.e: .

But I'd leave it as to be honest. Then it's just:

4. Express a+bi in terms of r(cos(theta + 2kpi) +isin(theta + 2kpi)). To find the fifth root, every term is to the power of 1/5 (in the case of arguments they're divided by 5) and then sub in different whole values for k to find the argument. Remember the argument has to be within minus pi and positive pi.
5. (Original post by the bear)
1+2i can be written as √5*ei*arctan2

so if a 5th root of 1 + 2i is w ....

w5 = √5*ei*arctan2

...
Do you prefer doing these questions with complex numbers in exponential form?
6. (Original post by B_9710)
Do you prefer doing these questions with complex numbers in exponential form?
i find it convenient... you can always do sin and cos later...
7. Thanks everyone!

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: April 3, 2016
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:
Today on TSR

### University open days

Is it worth going? Find out here

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams