You are Here: Home >< Maths

# complex numbers a level maths watch

1. can someone help me with this question:

1)z=-3+4i
given that z=(a+i)^4 where a is real find the values for a such that

z is real
z is wholly imaginary

2)
then, given that a+bi is the conjugate of (a+bi)^2 find all possible pairs of values for a and b.

not sure how to answer either question any help appreciated.
2. (Original post by trebor00)
can someone help me with this question:

1)z=-3+4i
given that z=(a+i)^4 where a is real find the values for a such that

z is real
z is wholly imaginary

2)
then, given that a+bi is the conjugate of (a+bi)^2 find all possible pairs of values for a and b.

not sure how to answer either question any help appreciated.
1: Begin with the binomial expansion of and then rearrange it into the form . From here, what do you need to make it real or wholly imaginary?

2: Expand and find its conjugate in the form , which is equal to . Then we may say and since we are equating real and imaginary parts.
3. (Original post by trebor00)
can someone help me with this question:

1)z=-3+4i
given that z=(a+i)^4 where a is real find the values for a such that

z is real
z is wholly imaginary

2)
then, given that a+bi is the conjugate of (a+bi)^2 find all possible pairs of values for a and b.

not sure how to answer either question any help appreciated.
Are you sure you posted the first question correctly?

z = -3+4i ?
4. (Original post by trebor00)
can someone help me with this question:

1)z=-3+4i
given that z=(a+i)^4 where a is real find the values for a such that

z is real
z is wholly imaginary

2)
then, given that a+bi is the conjugate of (a+bi)^2 find all possible pairs of values for a and b.

not sure how to answer either question any help appreciated.
For 1) I'm unsure what's the purpose of your defined at the start, but just expand your then make the real bit =0 for purely imaginary z, and then make the imaginary part =0 for purely real z.

For 2) Just expand it, and make it equal the conjugate of . Solve as required for pairs of values.
5. can someone show me how to do the first part of the first question as I still don't get it.
6. (Original post by trebor00)
can someone show me how to do the first part of the first question as I still don't get it.
Do you get how to expand ?
7. yes binomial expansion
8. (Original post by trebor00)
yes binomial expansion
OK, so I don't see how you're unable to do the question.

After expanding, you want to get your answer in the form of

For to be real, you want to set and find the values of which satisfy this.

For to be purely imaginary, you want to set instead.

### 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: November 12, 2017
The home of Results and Clearing

### 1,025

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. Bournemouth University
Wed, 22 Aug '18
2. University of Buckingham
Thu, 23 Aug '18
3. University of Glasgow
Tue, 28 Aug '18
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