You are Here: Home >< Maths

# complex equation watch

1. i need help with the following problem:
Find every z belonging to Complex, such that |z|=sqrt(5) and z^3-2z+16=3conj(z)
conj(a+bi)=a-bi
I multiplied by z on both sides of the equation, but didnt know how to go on from z^4-2z^2+16z=15.

Any help would be much appreciated.
Thank you, Paul.
2. (Original post by pbialos)
i need help with the following problem:
Find every z belonging to Complex, such that |z|=sqrt(5) and z^3-2z+16=3conj(z)
conj(a+bi)=a-bi
I multiplied by z on both sides of the equation, but didnt know how to go on from z^4-2z^2+16z=15.

Any help would be much appreciated.
Thank you, Paul.
Note that 1 and -3 are roots of your quartic, so you can take out factors of z+3 and z-1 from it.

Of course they don't satisfy |z| = rt(5) but the other two roots may do.
3. (Original post by RichE)
Note that 1 and -3 are roots of your quartic, so you can take out factors of z+3 and z-1 from it.

Of course they don't satisfy |z| = rt(5) but the other two roots may do.
Many Thanks. I could finish the exercise.

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: December 23, 2005
Today on TSR

Do you?

### University open days

• University of Lincoln
Mini Open Day at the Brayford Campus Undergraduate
Wed, 19 Dec '18
• University of East Anglia
Fri, 4 Jan '19
• Bournemouth University
Wed, 9 Jan '19
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