# Re(z) = 4Im(z)

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1. May 31, 2015

### Jess Anon

Find three different complex numbers that satisfy the equation in the form a + bi.

I know that:
Re(z) = a + bi = a
Im(z) = a + bi = b
Re(z) = 4Im(z)
a = 4b
I'm stuck after this point.
How do you find what is a and what is b?

2. May 31, 2015

### certainly

I don't understand the question.
For every $x$, the complex number $z=4x+ix$ satisfies $Re(z)=4Im(z)$
If you want three different ones, pick three distinct $x$.

3. May 31, 2015

### Jess Anon

I need the find the complex number z that satisfy the equation, therefore I do not think that using any 3 x is the correct way.

4. May 31, 2015

### certainly

Is $Re(z)=4Im(z)$ the only condition ?
If it is, then note that every $x$ satisifes the above condition with $z=4x+ix$.

5. May 31, 2015

### Jess Anon

That's alright.
z = 4 + i which means that it is 4 times the imaginary part of z.
Hence z = 4n + ni for any real value n.

6. May 31, 2015

### certainly

good for you :-)

7. May 31, 2015

### Staff: Mentor

In future posts, please follow the format of the homework template, with a complete description of the problem in part 1 (not in the thread title), any relevant formulas or equations in part 2, and your work in part 3. The use of the homework template is required for homework problems.

8. May 31, 2015

### Ray Vickson

You were asked to find three different complex numbers satisfying the given relationship. So, what is preventing you from just using three different numerical values of 'b' (choose any three you like) and then computing the corresponding values of 'a'?

9. May 31, 2015

### vela

Staff Emeritus
Just curious — in your mind, how is this different from what @certainly suggested, other than replacing the variable $x$ with the variable $n$?