You are Here: Home >< Maths

# Complex numbers help watch

1. Okay so i am kind of stuck in this question and i want to know the meaning as well as the answer behind it.
The complex number z satisfies the equation |z|=|z+2|.Show that the real part of z is -1 ?

I can do it graphical as z is V-shaped and |z+2| would mean x-2 and the point of intersection would be the answer
but i Think i forgot how to do it the normal way.?

Any help would be appreciated
Thankyou !
2. (Original post by Arsenal4lif)
Okay so i am kind of stuck in this question and i want to know the meaning as well as the answer behind it.
The complex number z satisfies the equation |z|=|z+2|.Show that the real part of z is -1 ?

I can do it graphical as z is V-shaped and |z+2| would mean x-2 and the point of intersection would be the answer
but i Think i forgot how to do it the normal way.?

Any help would be appreciated
Thankyou !
Write and then use Pythagoras stuff to remove the modulus signs.
3. Oh no.
Sorry man . I forgot Modula function.
Thanks
4. (Original post by JamesyB)
Write and then use Pythagoras stuff to remove the modulus signs.
This is a continuation of the same question

The complex number z also satisfies the equation |z|=2.By Sketching two loci in an Argand diagram , find the two possible values of the imaginary part of z and state the corresponding values of arg z.

So i drew |z|=2 and |z|=|z+2| .. I want to know the imaginary part they are asking are the intersection points of the two loci?
5. I just need some guidance pleease.
6. The modulus of is

Given that, think about the equation , which is:
7. (Original post by Arsenal4lif)
This is a continuation of the same question

The complex number z also satisfies the equation |z|=2.By Sketching two loci in an Argand diagram , find the two possible values of the imaginary part of z and state the corresponding values of arg z.

So i drew |z|=2 and |z|=|z+2| .. I want to know the imaginary part they are asking are the intersection points of the two loci?
Yes, that's what they're looking for. To get the exact values of the imaginary part and the argument you would need to use pythagorus and trigonometry.

### Related university courses

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: March 19, 2011
Today on TSR

### Exam Jam 2018

Join thousands of students this half term

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